text:
Coherent states and the quantization of 1+1-dimensional Yang-Mills theory
Four Dimensional Quantum Yang-Mills Theory and Mass Gap I: Quantization of the Solution of the Classical Equation
What is a precise mathematical statement of the Yang-Mills and mass gap Clay problem?
Infrared Gluon and Ghost Propagators
A theory of regularity structures
Exact solutions of classical scalar field equations
Functional determinant of a massive scalar field with variable mass
Introduction to Regularity Structures
Doubts about the theta angle and the ground state energy density in Euclidean Yang-Mills theory
Clarification: Why the gauge symmetry of pure Yang-Mills is $PU(n)$ and not $SU(n)$?
Energy-mass spectrum of Yang-Mills bosons is infinite and discrete
+ 4 - 2
Referee this paper: arXiv:0903.4727 by Alexander Dynin
Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)
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paper authored Mar 27, 2009 to Reviews I by (no author on PO assigned yet)
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see also http://www.physicsoverflow.org/21784/yang-mills-millenium-question-and-dynin-formalism
commented Aug 10, 2014 by Arnold Neumaier (15,458 points) [ no revision ]
I polished my earlier review to take account of the discussions and offline correspondence with the author (who still thinks he solved the problem).
see also the following article by L.D. Faddeev, http://arxiv.org/pdf/0911.1013v1.pdf
commented Apr 4, 2015 by Arnold Neumaier (15,458 points) [ no revision ]
see also the Report on the Status of the Yang-Mills Millenium Prize Problem by Douglas (from 2004).
commented May 13, 2015 by Arnold Neumaier (15,458 points) [ no revision ]
Your comment on this submission:
To review, leave an review instead. Comments are usually for non-reviews.
There are four (apart from rearrangements and minor changes) nearly identical papers claiming in different degrees to have solved the 7th Clay Millennium Problem.
Mass gap in quantum energy-mass spectrum of relativistic Yang-Mills fields
Alexander Dynin
Quantum energy-mass spectra of relativistic Yang-Mills fields in a functional paradigm
Quantum energy-mass spectrum of Yang-Mills bosons
The most recent paper (version v3 of the above listed first) claims at
the beginning of Section 1:
``A mathematically rigorous solution is given for both parts of the 7th Millennium problem of Clay Mathematics Institute''
This claim is wrong. Neither are the explicit requirements of the problem definition satisfied (not even a discussion of Poincare invariance and causality), nor is the paper mathematically rigorous in a crucial part of the construction (it is not proved that there is an operator with the anti-normal symbol specified in the construction).
In the following, I concentrate on the last (oldest) of these papers (more specifically its version arXiv:0903.4727v4) since I read this in most detail. However, it is easily seen that everything also applies to the more recent versions.
The paper starts with citing the short version of the formulation of the 7th Clay Millennium problem:
``Prove that for any compact (semi-)simple global gauge group,
a nontrivial quantum Yang-Mills theory exists on $R^{1+3}$ and has
a positive mass gap. Existence includes establishing axiomatic
properties at least as strong as the Wightman axioms of the axiomatic
quantum field theory. (Slightly edited)''
and goes on dismissing the second sentence of the requirement as impossible to solve, by reference to a 1993 book by Strocchi. The content of that book is widely known in the algebraic QFT community and was not overlooked when the authors of the millennium problem formulated it in 2000, as witnessed by their specific requirements. There seems to be be a misunderstanding on Dynin's part. Strocchi only argues that gauge fields cannot satisfy the Wightman axioms and would require an indefinite metric. However, Strocchi's arguments do not apply to local observable fields inside a quantum YM theory, namely to gauge invariant fields formed from gauge field strength (such as those mentioned in the citation below), are expected to satisfy the unaltered Wightman axioms in any valid construction of the vacuum representation.
The official statement in http://www.claymath.org/sites/default/files/yangmills.pdf says on p.5 explicitly:
A quantum field, or local quantum field operator, is an operator-valued generalized function on spacetime obeying certain axioms. The quantum fields act in a Hilbert space H that furnishes a positive energy representation of the Poincare group [...]
At any rate, for purposes of the CMI Millenium Problem, an existence proof for a quantum field theory must establish axioms at least as strong as those cited in [36, 29]. [...]
To establish existence of four-dimensional quantum gauge theory with gauge group $G$, one should define (in the sense of the last paragraph) a quantum field theory with local quantum field operators in correspondence with the gauge-invariant local polynomials in the curvature F and its covariant derivatives, such as $Tr F_{ij}F_{kl}(x)$. [...]
Correlation functions of the quantum field operators should agree at short distances with the predictions of asymptotic freedom and perturbative renormalization theory, as described in textbooks. Those predictions include among other things the existence of a stress tensor and an operator product expansion, having perscribed local singularities predicted by asymptotic freedom.
This leaves as minimal solution requirements (apart from the mass gap):
a positive energy representation of the Poincare group,
local quantum field operators in correspondence with $Tr F_{ij}F_{kl}(x)$,
correlation functions that agree at short distances with the predictions of perturbative renormalization theory,
the existence of a stress tensor and an operator product expansion, with the local singularities predicted by asymptotic freedom.
Dynin's papers do nothing towards a verification of any of these properties.
Now let us look at the content of paper arXiv:0903.4727v4. First two important claims made but nowhere substantiated by even a rudimentary discussion:
``The spectrum is both Poincare and gauge invariant.''
(last sentence of abstract)
This statement is nowhere discussed. One would need to quantize all generators of the Poincare group and the gauge group, not only the Hamiltonian, and show that the commutation rules survive intact.
The same unresolved difficulties as for the Hamiltonian quantization (discussed below) can be expected.
``As shown in the present paper the constrained initial data form an
infinite dimensional Kähler manifold'' (4th paragraph of Section 4.3)
To show this, the Kähler potential would have to be constructed, or a compatible symplectic and metric structure. No discussion of this appears in the paper. Since this only concerns the classical part, it can be fixed; all information needed is already there, just not spelled out.
I mention this as it gives valuable insight into Dynin's approach. Essentially, Dynin attempts to perform the geometric quantization of the infinite dimensional Kähler manifold mentioned.
Geometric quantization is the program of quantizing a classical theory given on a Kähler manifold. This works fully automatically and with full rigor for finite-dimensional manifolds, giving 1+0 dimensional quantum field theory (aka quantum mechanics). There it can be done neatly in a coherent state formalism called Berezin quantization. But its extension to infinite dimensions is at present more an art than a science. Even for field theories in 1+1 dimensions, it can at present be done rigorously only in nice, completely integrable cases.
The relevant manifold for the quantization of a classical field theoryis the manifold of solutions of the classical field equations, which is a symplectic space with the so-called Peierls bracket. For a classical theory with a well-posed initial-value problem, the space of solutions is parameterized by the space of initial conditions. In the case of a classical theory with constraints (gauge theories and general relativity), the initial conditions must satisfy a consistency condition preserved by the dynamics. Thus working with the manifold of solutions is equivalent to working with the nonlinear manifold of consistent initial conditions. This is the setting actually used by Dynin, and this explains why he discusses the unique solvablility of the Yang-Mills initial-value problem. (In fact, he makes nowhere use of these results; the quantum part is completely independent of the classical existence results.)
To proceed in analogy with the finite-dimensional case one needs to equip the symplectic manifold with a Kähler structure and a Liouville measure, construct the corresponding coherent states, and express the operators to be quantized (in this case the generators of the Poincare group and of the gauge group), by defining consistently how they operate on the coherent states. Then one must check their commutation relations and resolve any anomalies that might be encountered in this process.
Dynin skips the Kähler structure and goes directly to the coherent states (from which the former can probably be obtained). The coherent states are constructed in the terminology of white noise calculus and Hida distributions, unfamiliar to physicists but equivalent to the standard second quantization formalism. (Comparing the action of creation and annihilation operators on Glauber coherent states with the formulas (40)-(44), one sees that $\hat\xi$ is an annihilation and $\hat\xi^\dagger$ a creation operator; the normal (antinormal) symbol is in a physical coherent state context the lower (upper) symbol or Q-(P-) representation. Making mentally the corresponding changes makes the paper much more readable.)
Dynin's notation is further obscured by adhering to a rarely used form of the Einstein summation convention, applying it to drop from the notation every functional integration over fields appearing twice. This makes the definition of the quantization operations in (45) look harmless, whereas in fact they involve a functional integration over the field $\zeta$.
This is the source of a gap in the later construction of the quantization of the Hamiltonian. Dynin quotes theorems stating the existence of the various symbols for every continuous operator from the bottom to the top of the Gelfand triple defining the Fock space of interest. However, this direction (from the operator to the symbol) is dequantization, while later he utilizes the opposite direction (from the symbol to the operator) for quantization. This direction is used in (64) unsupported by quoted theorems and in fact unsupported by any discussion.
As a consequence, it is unproved that an operator exists whose antinormal symbol is (64), only that if it exists it is unique. Since the operator in question is the putative quantized Hamiltonian, its existence is unproved.
This is the essential gap in the construction.
Note that the lack of rigor doesn't come from using a path integral, which is indeed a well-defined concept in stochastic calculus, but that he doesn't check whether the path integral he needs is actually convergent.
In fact, I think the gap cannot be cured without importing further ideas.
For by the theorems quoted, each good operator has all three symbols. Thus it should be possible to reorder the Hamiltonian with antinormal symbol (64) to normal form. But it seems to me that this produces infinite coefficients, which would show that the construction is faulty, i.e., the Hamiltonian would not exist. This would ruin the quantization program; and indeed this is the point where all rigorous techniques stumbled so far. Additional nonperturbative renormalization techniques would be needed to fix the gap.
However, if the Hamiltonian could be proved to exist, the remaining discussion appears to be valid. In particular, the discussion surrounding (75)-(76) would be consistent with the existence of a single massive particle and a dynamics that preserves the number of such particles and leads to scattering only within each sector.
Finally, note that there is also a published paper on massless QCD, which shares the virtues and flaws of the papers discussed here:
Alexander Dynin,
Quantum Yang-Mills-Weyl Dynamics in Schroedinger paradigm,
Russian Journal of Mathematical Physics 21 (2014),No.2,169-188.
reviewed Aug 9, 2014 by Arnold Neumaier (15,458 points) [ revision history ]
edited Aug 17, 2014 by Arnold Neumaier
This review is completely wrong. There is no "gap" or "missing lemma" or "nonrigorous ambiguity" in this paper, it is simply garbage.
You are WRONG about the formalism of white noise calculus and Hida distributions! First, it is familiar to physicists, in the cases where they are used in this paper, they are equivalent to creation and annihilation operators, i.e. "second quantization of free field theory". They are NOT equivalent to second quantization in general, just to creation and annihilation operators of free field theory. They don't serve to define the path integral, as they do no renormalization.
A proper formalism to do this is provided by Harer's "regularity structures", which actually takes the limit of white noise stochastic stuff to the continuum doing an appropriate renormalization along the way.
Further, in this paper, the white noise calculus is used to define free-field style creation and annihilation operators on objects which are classical field theory solutions! It has absolutely no relation to second quantizing Yang-Mills theory.
The paper does not have small flaws, it has an ENORMOUS flaw that the formalism it uses does not bear any relation to the quantum theory which it is attempting to describe.
While you are right that there is an implicit path integral in the Einstein summation convention in the paper, you are wrong that this renders the paper non-rigorous. The implicit path integral in this case is interpreted in the stochastic formalism, and so the results that are obtained are not problematic, they are results which are true for quadratic path integrals. It's just that the author lifted these results by defining creation and annihilation operators associated to classical solutions, and declaring this to be a quantum field theory of Yang-Mills type!
It's really what I said in my answer, and really, there is nothing non-rigorous in the stuff he is doing--- he is using standard theorems from stochastic mathematics, just applying them to a new model which is essentially free particles indexed by solutions to classical equations, rather than anything to do with quantum field theory.
Further, the program of symplectic quantization is deeply flawed in the case of field theory, and there is no theorem, or even heuristic, that suggests that any field theory with a nontrivial running can ever be described by symplectic quantization. The reason is simply that the classical equations at short distances bear no relations to the long-distance properties of the typical configurations in the path integral, which in the case of QCD randomize everything.
If you would like to show that symplectic quantization works, I would suggest to first do the same thing in 2+1 dimension $\phi^4$ theory, where we have a rigorous Glimm-Jaffe description, recently reproduced by Harer. This arena allows you to see whether the quantum $\phi^4$ theory (much simpler than QCD) can be described in any way from the solutions to classical $\phi^4$ theory. The answer is obviously "no", since the coupling runs in the quantum theory, and doesn't run classically, but I'll let you figure that out yourself.
The stuff in this paper is nothing remotely resembling any sensible description of QCD, it is a crazy paper.
commented Aug 9, 2014 by Ron Maimon (7,720 points) [ no revision ]
In mathematical physics (and this is supposed to be a paper in this area), second quantization always means "second quantization of free field theory"; no matter what more general usage there may be elsewhere.
In nonrelativistic quantum field theory, where no renormalization is needed, it is clear that the Hamiltonian dynamics happens in the Fock space obtained by second quantization of a system of infinitely many harmonic oscillators. The dynamics has nothing to do with this Fock space - all field theories with the same free field content have the same Fock space as Hilbert space. The dynamics depends solely on the Hamiltonian defined on it.
All (relativistic or nonrelativistic) Hamiltonian approaches to quantum field theory start with such a Fock space, though often on a lattice befoire taking the continuum limit.
Since Dynin is taking a Hamiltonian approach, it is natural that he starts with a Fock space, too. His Fock space (27) is the Fock space whose configuration space is the space of all (nice) functions on the classical space (23) of constrained Cauchy data. This space has no intrinsic dynamics, as the Cauchy data are given at $t=0$ only.
Thus your claim that he employs creation and annihilation operators on solutions is as unfounded as claiming that the Fock space of a single harmonic oscillator mode - in which an anharmonic oscillator is studied - acts on solutions of the classical anharmonic oscillator.
commented Aug 9, 2014 by Arnold Neumaier (15,458 points) [ no revision ]
The lack of rigor doesn't come from using a path integral, which is indeed a well-defined concept in stochastic calculus, but that he doesn't check whether the path integral he needs is actually convergent.
The lack of rigor is thus like that of integrating $e^x$ over the real line, based on the background knowledge that the Lebesgue integral has a meaningful definition. It has for integrable functions, but not for this particular case.
Had Dynin shown that the path integral exists in the case he needs it, the paper would have been rigorous, but he hasn't shown it. And I believe he cannot show it.
''the classical equations at short distances bear no relations to the long-distance properties of the typical configurations in the path integral, which in the case of QCD randomize everything.''
This is irrelevant for Dynin's approach as he makes no use at all of classical solutions. If one removes the discussion in Section 2 about classical solutions, his remaining arguments remain completely unaffected.
Thanks Arnold, This review seems to fit the bill properly. I would like to hear from the author. I wrote to him with no avail. I think that could be satisfactory also as an answer for MO.
commented Aug 9, 2014 by JonLester (345 points) [ no revision ]
The formalism he is using does not define anything like a gauge theory, this is not an arguable point. The raising and lowering operators he is using are defining "states" indexed by integers which are nothing like the states of gauge theory anything.
These integer indexed states are associated to solutions of the classical theory, but they have no relation to actual quanta of anything! This is the way he proves the "mass gap", by bounding the "energy" by "N" the excitation number.
The (nonsensical) procedure is exactly as I said, and upon further reading you will realize this is so.
edited Aug 9, 2014 by Ron Maimon
By the same argument it would follow that, for any field theory, the states in canonical QFT via second quantization in Fock space defines integer-indexed states that have no relation to actual quanta of anything. In canonical quantization they are the bare building blocks of the renormalized theory.
Dynin's renormaization recipe is inadequate, but his state space is as good as that of any of the 4D state spaces considered in the literature.
commented Aug 10, 2014 by Arnold Neumaier (15,458 points) [ revision history ]
That's right! The free-field quanta have no real relation to the actual states of the theory, this is the essence of that theorem in the 1960s that the free-field Hilbert space and the interacting field Hilbert space are not related unitarily.
The description starting from fock-space is only roughly ok for getting the basic picture in weakly interacting field theory. In this case, even if he were to do the quantization right, he would be getting gluon fock states, with an N=0 vacuum consisting of no gluons, around the solution gauge field=0.
This would not have any relation to the actual ground state, which is a randomly twisting gauge field every which way, and consists of N=infinity gluons even in the vacuum. The only place a fock-description of gluons is roughly appropriate is in a short-distance bag, at long distances there are lots of 'wee gluons', infinitely many particles.
The N=0 vacuum is nonsense in this case. But the paper makes worse nonsense. In this paper, the quantized states are not really fock states at all, they are free-field raising lowering operator fock states with no relation to the actual theory one is trying to quantize, they are just a tower of states associated to classical solutions. They are total nonsense, they don't even define the wrong ass perturbative vaccuum for gauge theory, they are nothing at all.
commented Aug 10, 2014 by Ron Maimon (7,720 points) [ no revision ]
Here is the answer by Alexander Dynin that I post on his behalf:
The Schroedinger paradigm in QFT is a quantization of functionals on the initial data. Under certain conditions the latter parametrize the solutions of classical YM equations but not the latter are quantized. Functionals may be non-linear but the Shroedinger operator is linear of course. No disentanglement is required.
Certainly, my procedure  is not relativistic but the energy-mass component of the classical relativistic  energy-momentum vector is not either. That is very important. In particular,  Poincare generators have no role here even when an  action functional is relativistic. The  results are the same qualitatively in all  Lorentz coordinates.
The energy-mass functional is a tame polynomial in infinite dimensions. As such it is a symbol of a tame operator in the  Gelfand-Kree triple and defines an unbounded self-adjoint operator in the corresponding Fock space. As such  the quantum Yang-Mills operator does exist.  My latest main theorem about the structure of its spectrum achieves  much more  than a solution of the YM mass gap problem.
commented Aug 13, 2014 by JonLester (345 points) [ no revision ]
Hi @Polarkernel, do you have an idea why neither I nor JonLester who posted it can edit this comment? The formatting should be improved ...
commented Aug 13, 2014 by Dilaton (6,040 points) [ no revision ]
Repost for readability.
@Polarkernel I try reposting with identical results. The problem can be traced back to Thunderbird where there is no carriage return to end a line neither line feed. So, the line is never formatted. But it is not clear why there is no possibility of editing.
@JonLester: Please copy the message from Thunderbird into an ASCII editor and add there the line feeds before copying it into the comment window.
@JonLester Sorry, but I have to investigate what happens here. To do this, I have to download a backup of the database and load it into my local site. This will take a while. I hope you can solve it using the proposition of Arnold Neumaier.
commented Aug 13, 2014 by polarkernel (0 points) [ no revision ]
@Polarkernel @Arnold Thanks, I'll do so. @ArnoldNeumaier meanwhile you can check MO where I posted as well and worked fine.
The Schroedinger paradigm in QFT is a quantization of functionals on the initial data. Under certain conditions the latter parametrize the solutions of classical YM equations but not the latter are quantized. Functionals may be non-linear but the Shroedinger
operator is linear of course. No disentanglement is required.
Certainly, my procedure is not relativistic but the energy-mass component of the classical relativistic energy-momentum vector is not either. That is very important. In particular, Poincare generators have no role here even when an action functional
is relativistic. The results are the same qualitatively in all Lorentz coordinates.
The energy-mass functional is a tame polynomial in infinite dimensions. As such it is a symbol of a tame operator in the Gelfand-Kree triple and defines an unbounded
self-adjoint operator in the corresponding Fock space.
As such the quantum Yang-Mills operator does exist.
My latest main theorem about the structure of its spectrum achieves much more than a solution of the YM mass gap problem.
While Dynin may think that Poincare invariance is irrelevant, it is one of the conditions of what it means to have solved the millennium problem. That he chooses not to address the issue means that he chooses his work not to be eligible as a solution of the millennium problem. Moreover, it is unacceptable that he claims under these circumstances in the abstract that the spectrum is Poincare-invariant without devoting later a word to it.
I also don't believe his statement that an operator with the given anti-normal symbol exists. At least the results he actually cites in his paper (the oldest or the newest) do not prove it (whereas some results that he cites are not even used). The least Dynin should do is to point precisely to the results from the literature needed to prove it, so that one can check his claim. He should also explicitly evaluate the corresponding normal symbol to prove me wrong, since I think it is infinite.
Dear @ArnoldNeumaier, I post these answers by Dynin for your consideration. Alexander knows you as a mathematician and so he addresses this to you:
I refere to my latest version 1009.3779v4 [math-ph] which is a reedited my published paper to make exact reference to YM millennium problem.
The Clay official statement includes establishing axiomatic properties at least as strong as Wightman axioms of quantum field theory, not the Wightman axioms per se. In his own statement cited in the preprint, E. Wittendoes not mention them at all. There is nothing about Poincare invariance in my abstract. Even in general relativity the non-relativistic initial values problem is a very important tool for existence of solutions of general Einstein equations. In my case the dependence of the YM spectra does not depend on Lorentz coordinates.
I designate the energy-mass functional of constrained initial data as the the anti-normal symbol of quantum Yang-Mills operator. On transverse YM fields it is explicitly simplified to the formula (69). The latter is a continuous polynomial functional on the transverse test space \(\mathcal{H}^\infty\) so that the quantum YM operator with such anti-normal symbol is well defined as a continuous non-negative operator in \(\mathcal{K}^\infty\) (because it is a continual linear combination of the pointwise operators of creation and annihilation that have this property). As such the YM operator is essentially self-adjoint and I use its Friedrichs self-adjoint extension with a well defined spectrum.
My text is self-contained modulo well established mathematics. In the preprint I provide precise references.
Alxander
1. The 2009 paper (which is the one that I refereed) contains as last sentence of the abstract the claim about Poincare invariance.
''at least as strong as Wightman axioms'' means to a mathematician that the latter must be deducible. These include Poincare invariance and causality.
Even if the requirements were interpreted in a more generous sense I don't see any verification of axiomatic properties of any kind, with a discussion of why these should be regarded as being ''at least as strong as Wightman axioms''.
2. (63) in the 2009 paper defines a functional supposedly defining an operator that has this functional as its antinormal symbol. The reason why this operator exist cannot be something being ''a continual linear combination of the pointwise operators of creation and annihilation'' - using the properties of the operator to be constructed as proof for its existence is unsound circular reasoning.
3. If the paper is self-contained: Where are the definition of tameness and its properties? Where is a sufficiently strong condition on a functional that guarantees that it defines an operator with this functional as antinormal symbol? (Does the tameness of a functional imply existence of this operator?) Where is the reference to a proof of this statement? And where is the verification that (63) satisfies this criterion? None of the three is present.
4. The 2010 paper 1005.3779v4 [the number in the Dynin's reply has a misprint] is irrelevant in the present context as it is not about YM quantization but about massless QCD. But its equation (69) is essentially the same as equation (63) in the 2009 paper commented on above. The existence of ${\mathbb Y}:=\widehat Y_\alpha$ at the bottom of page 19 is assumed without sufficient justification.
''The Clay official statement includes establishing axiomatic properties at least as strong as Wightman axioms of quantum field theory, not the Wightman axioms per se. In his own statement cited in the preprint, E. Wittendoes not mention them at all.''
The official statement in http://www.math.vt.edu/people/gao/physics/yan-mills/yang_mills.pdf says on p.5 explicitly:
A quantum field, or local quantum field operator, is an operator-valued generalized function on spacetime obeying certain axioms. The quantum fields act in a Hilbert space H that furnishes a positive energy representation of the Poincare group [...] At any rate, for purposes of the CMI Millenium Problem, an existence proof for a quantum field theory must establish axioms at least as strong as those cited in [36, 29].
To establish existence of four-dimensional quantum gauge theory ... Correlation functions of the quantum field operators should agree at short distances with the predictions of asymptotic freedom and perturbative renormalization theory, as described in textbooks. Those predictions include among other things the existence of a stress tensor and an operator product expansion, having perscribed local singularities predicted by asymptotic freedom.
Thus without the verification of these properties Dynin might have constructed something, but has definitely not solved the challenge of the Millennium problem.
This paper gives a false construction, it proves theorems about a quantum system of no interest, whose kinematics is defined by a tower of harmonic-oscillator excitations labelled by classical solutions of Yang-Mills theory. These excitations have nonlinear interactions with themselves, but not with each other. Nothing about this construction has anything to do with quantum Yang-Mills theory, or with any field theory of any kind.
To explain what is going on, consider a free scalar field, with a mode-wise self-interaction between each mode and itself, as in the following quartic interaction:
$$H_0 = \int_k a^\dagger_k a_k dk$$
$$\phi_k = a^\dagger_k + a_k$$
$$H_i = \int_k \phi_k \phi_k \phi_k\phi_k dk$$
With appropriately relativistically normalized creation and annihilation operators, and appropriate relativistic measure. Notice that the spectrum of each mode is still discrete, you can prove this rigorously very easily, and also notice that each mode is still free.
For quantum fields, the interaction Hamiltonian links different modes:
$$H_i = \int \phi_{k_1} \phi_{k_2}\phi_{k_3}\phi_{k_4} \delta(k_1+k_2+k_3+k_4) dk_1 dk_2 dk_3 dk_4$$
With appropriately normalized delta function. This is what leads to scattering, and interactions.
The formalism Dynin uses is that of free-field creation and annihilation operators, and in his paper, these operators are indexed by the space of classical solutions, so they act to produce a free-field tower of excitations indexed by the occupation number integer N for each classical solution to the Yang-Mills field equations. Dynin then uses these towers to provide the kinematics of his purported construction of quantum Yang-Mills.
Such a construction, starting with a tower of occupation numbers on each classical solution, is a-priori impossible on general grounds. It is will known that the state space of an ordinary relativistic interacting theory has no unitary relation to the free Fock space of a free field theory, there are, if you like an intuitive picture, infinitely many virtual particle in the vacuum simply by translation invariance, so that even a finite density of virtual particles is an infinite number of particles overall, in infinite volume. This is the classical Haag theorem, which is very easy to prove.
The construction in this paper violates the Haag theorem, because it has a kinematic space which doesn't change depending on the coupling constant, the vacuum is the same in the interacting and free versions, and so it is manifestly incorrect.
But the construction is even more problematic than this, in that the creation and annihilation operators are indexed by the space of initial conditions, so that there is a separate operator for each initial condition. This is not even the correct kinematics for free field theory, where the creation and annihilation operators are indexed by modes of the initial conditions--- there is one photon creation/annihilation operator for each mode of a box, not for each initial condition. The photons corresponding to an initial condition are mixtures of the photons corresponding to the mode decomposition of this initial condition. The kinematic space described here is even more incorrect than just being identical in the free and interacting cases, it is introducing too many creation and annihilation operators.
To understand just how different the free and interacting Fock spaces are in Yang-Mills, is worthwhile to review the expected behavior of quantum Yang-Mills theory from the numerical simulations of lattice Yang-Mills, and the strong-coupling behavior discovered by Wilson in his 1974 paper introducing Lattice Gauge Theory. When you place a coarse lattice over the continuum Euclidean lattice theory and consider the holonomy along the links of the lattice as your variables (standard lattice gauge theory), assuming the scale of the lattice is much greater than the confinement radius, the gauge field becomes entirely random! The correlations of the link-matrices converge to zero. The convergence is exponentially fast at scales larger than the confinement radius $\Lambda^{-1}$.
The approach of the long-range lattice field to a random field means that any naive description of the vacuum in a picture starting from the kinematics of a free field theory necessarily fails in a way much worse than in traditional QED. A random-gauge vacuum contains infinitely many soft gluons, the notion of a single gluon no longer exists. The Haag theorem is not particular to gauge theory, but in the case of gauge theory, the nontrivial vacuum is especially striking, because the long-range statistically random Euclidean gauge field has no relation to the classical Euclidean vacuum of everywhere zero gauge field, up to gauge transformations.
Putting aside general considerations, one can examine the specific arguments in the paper. The sections dealing with classical Yang-Mills are uncontroversial and unoriginal, they are summarizing previous results about the classical theory. The quantization formalism of this paper introduced in section 3.2 is using a mathematically rigorous version of the traditional creation and annihilation operators, where the coherent states are used as the non-orthonormal eigenstates of the annihilation operator. This is reviewed in physics sources in several places under the keyword coherent state path-integral.
The formalism on page 13 defines normal ordered products of field operators. The normal ordering is a bit obscured by the unfamiliar notation, but you can see the effect of the normal ordering multiplication on the bottom of page 13, and in particular, in proposition 3.2, which claims that the operators preserve the vacuum.
The claim that the N=0 state is still the vacuum is a mistake. When you normal order the interactions, you can make the N=0 state preserved by the interaction, but you are doing something extremely non-covariant, something which has no relation to relativistic quantum field theory. You are choosing a reference set of free-states relative to which you define your normal ordering, and defining the vacuum and dynamics relative to these reference states.
The proof of mass gap is then by rearranging an intermediate-step number-type operator defined to bound the energy from below from anti-normal ordered, to normal ordered, introducing a 1/2, just as in the Harmonic oscillator ground state energy, while the rest is positive definite. This is incomprehensible, because the rearrangement is done on a single mode only, using the fact that each mode is only interacting with itself, much as in the scalar example I started with.
This is a complete rewrite of an earlier review, in which I made a mistake, caused by working backward from equation 73. First, I saw that the vacuum is preserved by the form of the interaction, and the interacting theory would be unitarily related to the free one if the construction is correct. Since this is impossible in an interacting relativistic field theory, I assumed that the theory is free. Since equation 73 is simply reordering the Hamiltonian to introduce a 1/2, like the ground state energy of a Harmonic oscillator, I falsely deduced that Dynin's unjustified assumption is that the energy is the number operator times the classical energy. This is not the case. Dynin's mode-energy contains interactions, the actual unjustified assumption is that each mode only interacts with itself, so that he can do the rearrangements mode by mode to get a discrete spectrum for each mode.
The Hamiltonian in section 3.2 is manifestly not free, but it also manifestly only connects each mode number-operator tower with itself, it does not lead to interactions between different modes. This is a serious error, and there are no potential applications of this analysis to any field theory.
reviewed Aug 9, 2014 by Ron Maimon (7,720 points) [ revision history ]
edited Apr 11, 2015 by Ron Maimon
+1. Judging from the propositions he posed(I'm not yet able to figure out the detailed mathematics, although they largely look like a formalization of what I already know), I completely agree with you. Just let me try to repeat the points in my own words to see if I misunderstand anything:
Firstly the author put Cauchy data of YM equation as the "wavefunction(al)s" to construct the Hilbert space, but then the apparent paradox is that according to YM equation, these wavefunctions evolve nonlinearly in time, but to be qualified as Hilbert space vectors, they have to evolve linearly in time, I don't see the author addressing the obvious paradox anywhere in the main article, except in the signpost section 4.3, a very brief discussion is given, where I can't extract too much useful information. To try my best, by equation (77) it seems the author forced the wavefunctions to evolve linearly, ignoring the nonlinear character of YM equation, the result probably is a free field dynamics(not sure if this is right after second thought. Actually, @RonMaimon, are you sure the resulting theory is a non-interacting one? It seems as long as the Hamiltonian constructed is not trivial, it has a chance to contain non-trivial scattering).
Secondly, claiming proposition 3.3 implies a mass gap is astonishingly absurd, to me it at best implies the spectrum is bounded below.
Update on 15/April/2015: After reading Arnold I'm convinced I didn't understand Dynin's content at the first read, due to the unfamiliar notations Dynin used. Hence my comment above the dashed lines is most probably a result of confusions.
commented Aug 9, 2014 by Jia Yiyang (2,640 points) [ revision history ]
edited Apr 14, 2015 by Jia Yiyang
Actually, I'm inspired to ask: Do classical solutions of YM equation have any bearing on the quantization? What is it?
commented Aug 9, 2014 by Jia Yiyang (2,640 points) [ no revision ]
Ron, the paper is not rubbish, although it falls short of its claims. Please read the paper more carefully. At least one of your claims is simply wrong: You write
Since the author defines the "quantum energy" as the occupation number times the classical energy, it concludes that any state with occupation number 1 always has C more energy than the "vacuum", with occupation number zero.
but this is not what he does. The number operator (60) is quadratic in a/c operators, while the Hamiltonian (64) is quartic. He uses the number operator only to get a lower bound on the Hamiltonian spectrum, resulting in Theorem 3.1, which says the spectrum is discrete and bounded below by a shifted occupation spectrum.
This is a misunderstanding. In (77), H must be an operator on functions of histories (as the next line suggests), otherwise the equation doesn't make sense at all. Thus the linear dynamics is in the space of all linear combinations of coherent states, as in all QFTs (even the free ones). The flaws of the paper lie elsewhere, not in these superficial problems due to the fact that Dynin uses notation unfamiliar to physicists.
Dynin does not quantize the space of classical solutions; in fact, the construction in Sections 3 and 4 does not make use of any of the results about classical solutions.
Instead, he quantizes the space of initial conditions! This is the same procedure we follow in quantum mechanics and in nonrelativistic quantum field theory. The Hilbert space is the space of functions on zero time configuration space.
For everything else see my review.
Here it doesn't necessarily involve any inconsistency, because creation/annihilation operators can be understood as operator-valued functionals: if the amplitudes of the Fourier modes of the initial condition is $f(k)$, then $a^\dagger(f)=\int dk f(k) a^\dagger(k)$, where $a^\dagger(k)$ is the creation operator that creates a photon with definite momentum $k$. So "creation and annihilation operators are indexed by the space of initial conditions" could really be just a fancy way of saying you can superimpose $a^\dagger(k)$'s to get a new creation operator. This contains no more and no less information than what we physicists are already familiar with.
commented Apr 14, 2015 by Jia Yiyang (2,640 points) [ revision history ]
@JiaYiyang: Indeed, that could have been what he was doing, and then it would have been the correct free-field kinematics, but it's not. When he constructes the Hamiltonian with the "a breves", he replaces the values in the classical energy function with operators specific for the given initial condition, the replacement of a-breves by a's consitute the quantization procedure, and this replacement makes "interactions" (i.e. quartic terms) which contain a-a-a-a products for one given set of initial conditions only, i.e. each initial condition interacts only with itself. Since each initial condition is a separate a and a-dagger, a separate Harmonic oscillator, he can then do formal rearrangements on the quartic term and show that the spectrum is discrete and gapped solution by solution. But he never has products of operators linking together different modes, as when you have this, you immediately get infinite integrals over a mode-index when you try to rearrange the nonlinear terms, and you get all the normal behavior of quantum field theory, like nontrivial vacuum, and divergent expressions.
Each separate initial condition is a completely disconnected excitation tower whose interactions are not linked to any other tower, and the kinematics is much larger than the correct kinematics you describe in the statement above. This is disguised by the formalism--- it would be possible in the same formalism to do things right, but that's not what he does.
This is exactly what confused me in the first iteration of the review. I noticed equation 73 is rearranging creation and annihilation operators, as if he is dealing with a single decoupled Harmonic oscillator. So I assumed that the Hamiltonian is free because each creation/annihilation tower was disconnected from all the others, since he is rearranging the operators which in free field theory would normally correspond to one mode independently from every other mode. This is a property of mode-operators in free-field-theory, and not in interacting field theory. But his mode theory is not free, there are quartic terms, but these quartic terms after quantization only talk about the a's associated with a single solution, they don't multiply the a's of separate solutions, so the end result is still a completely disconnected set of anharmonic oscillators, one for each initial condition.
If he had made the identification that different initial conditions have a's which are not distinct, he wouldn't be able to rearrange the operators like in 0+1 d perturbations of the HO, as he would get integrals over k from the products of coinciding operators, as usual.
commented Apr 14, 2015 by Ron Maimon (7,720 points) [ revision history ]
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redpajama_set_name: RedPajamaCommonCrawl


text:
Pak conveys 'concerns' on acquittal of Samjhauta blast 'perpetrators'
By topstoryeditior On Mar 22, 2019
Islamabad [Pakistan], Mar 22 (ANI): Pakistan, on Wednesday, conveyed concerns regarding the acquittal of the four suspects in the 2007 Samjhauta Express blast case to other countries through its Foreign Secretary Tehmina Janjua.
Janjua invited members of diplomatic corps to the Foreign Office and briefed them on the "historic injustice done to the forty-four Pakistanis killed in the Samjhauta Express terrorist attack in 2007 in India," according to The Express Tribune. A special NIA court had acquitted the four suspects – Swami Aseemanand, Lokesh Sharma, Kamal Chauhan and Rajinder Chaudhary – in the case on March 20.
"Pakistan has already registered a strong demarche with the Indian High Commissioner on March 20 against the acquittal of the perpetrators of Samjhauta terror attacks," the Foreign Secretary said.
On February 18, 2007, explosions hit the India-Pakistan trans-border Samjhauta Express in Panipat area of Haryana and 68 people died in the blast, including scores of Pakistanis.
Out of the deceased, 33 were male, 19 female and 16 children. Later, two unexploded bombs were also found from the site, India's National Investigation Agency (NIA) had said.
The Indian side has earlier rejected Pakistan's assertions, after its High Commissioner to Pakistan was summoned following the March 20 decision. It was put forth that due process of law was followed by the Indian courts and judicial system in a transparent manner, according to sources.
In fact, the High Commissioner called out the lack of cooperation from Pakistan government, including in serving court summons to Pakistan witnesses in the Samjhauta blast case. The summons were returned by Pakistan's Foreign Office and not served, sources said.
The High Commissioner asked for an expeditious trial in 26/11 Mumbai terror attacks in which detailed evidence has been given to Pakistan. He expressed disappointment that progress in these trials is held up and the perpetrators and prime accused continue to roam freely in Pakistan, sources further said.
He shared India's concerns at the lack of progress in investigations in Pathankot airbase terror attack even when JIT visit was arranged to India and detailed evidence shared, they added.
It was also pointed out that Pakistan is yet to take credible and irreversible steps against Jaish-e-Mohammad (JeM) other terror entities and individuals, despite a detailed dossier having been shared after Pulwama attack, sources said. (ANI)
topstoryeditior
India not to attend Pakistan National Day celebrations after Separatists leaders get invited
Tom Ford calls out fake quote targeting Melania Trump
एओए के चुनाव में 9 लोग हुए विजयी
BJP to repeat govt. In Gujarat, Himachal Pradesh; AAP to emerge strongly in Delhi MCD…
CEC Rajiv Kumar invited as International Observer for forthcoming Elections in Nepal
Khursheed', a celebration of Urdu Poetry by Fauzia Arshi


text:
Back to Media Room
Wreckshop Nation Launches New Four-Part Docu-Series Titled 'Sound of the City'
'Sound of the City' gives viewers a behind-the-scenes look at what it takes to produce an album by following the creation of Wreckshop Nation's collaborative new project titled 'Unity Vol. 1.' The docu-series premieres Sept. 17, 2018.
Press Release - updated: Sep 10, 2018
HOUSTON, September 10, 2018	(Newswire.com) - In a penetrating world of hip-hop and pop music, there is no denying the effect that Southern, specifically the "Deep South," music has made on the culture. Houston, Texas is the home of various underground rap masters, many of whom paired their non-traditional business-savvy and street smarts to grab the attention of the mainstream audience which eventually created a movement in hip-hop that is still thriving today.
Powerful independent labels such as Rap-A-Lot and Swisha House cultivated the market and birthed pioneering recording acts such as the Geto Boys, UGK and Slim Thug. But in the heart of the Screw Movement stood a label that created the true foundation of today's Houston music scene, taking its rightful place among the list of esteemed labels: The Legendary Wreckshop Records.
Known as one of Houston's leading independent record companies, Wreckshop collectively sold over 2.5 million albums in five years, a number that was not seen amongst independent labels at the time. Its ambitious founder and visionary Derrick "D-Reck" Dixon started Wreckshop Records in 1997.
Wreckshop Nation was and still is a driving force in the music industry and industry insiders cannot help but take notice. Now, to be more innovative than ever, the record label launched itself into a new direction by creating a four-part episode docu-series or web series called "Sound of the City."
"Sound of the City" gives viewers a behind-the-scenes look at what it takes to produce an album by following the creation of Wreckshop Nation's collaborative new project titled "Unity Vol. 1." With the upcoming release of "Unity Vol. 1," a project produced by DJ X-O featuring Houston's hottest emerging artist, Wreckshop Records will always be a major staple in Houston's music scene and will forever be respected throughout the South. Though Houston's talents, as well as their accomplishments, sometimes go under the national radar, there is no denying the impact that this independent record label has created for music overall.
The four-part docu-series is set to premiere on Sept. 17, 2018.
To tune in to watch "Sound of the City" or for more information on Wreckshop Nation, please visit https://www.wreckshopnation.com/.
For media or press inquiries, please contact media relations at press@lemonlimelightmedia.com.
About Wreckshop Nation
Wreckshop Nation (WSN) is an independently owned entertainment company focused on promoting and producing digital content, products and services for artists while simultaneously embracing the Southern Hip-Hop culture that developed in Houston during the late 1990s - the "Wreckshop Records" era - and still thrives today.
Wreckshop aims to be more than just a label, but a brand; it is striving to be a centralized platform that hosts all forms of digital content related to the Southern Hip-Hop culture, both old and new.
WSN CEO Derrick "D-Reck" Dixon has used his industry contacts to establish a powerful network of professionals who can help promote artists who collaborate with the platform and takes pride in his ability to reach the success that he visualizes for both himself and his clients.
Above all else, Wreckshop Nation values brotherhood, companionship and independence, and has built its foundation upon these values so that it can unite and serve the Southern Hip-Hop community as effectively as possible.
For more information on Wreckshop Nation, please visit https://www.wreckshopnation.com/.
Source: Wreckshop Nation
Categories: Arts and Entertainment
Tags: DERRICK-D-RECK-DIXON, HOUSTON-TEXAS, INDEPENDENT-RECORD-COMPANY, MUSIC-INDUSTRY, SOUND-OF-THE-CITY, SOUTHERN-HIP-HOP, WRECKSHOP-NATION, WRECKSHOP-RECORDS
About iBoss Media
View Website or Media Room
iBoss Ventures is a strategic holding and startup consulting firm with a focus on equipping entrepreneurs in the tech, media, gaming, information, and entertainment industries with proper management and tools for optimal venture success.
Dana Blickensderfer
Co Founder, iBoss Media
moc.latigidssobi@anad
iBoss Media
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Midtown Medical and Titan Imaging Sponsor Personal Injury Networking Event
Midtown Medical and Titan Imaging are sponsoring a Nashville personal injury networking event on Thursday, Nov. 7, 2019, at Ruby 2411 Blakemore Ave. Nashville, TN 37212 from 6-9 p.m. Text RSVP to Jason Ashley at 404-985-0372.
iBoss Media - Nov 5, 2019
Marquis Medical Center Hosts Grand Opening for New Birmingham Location
Marquis Medical Center invites chiropractors, attorneys, physical therapists, and all from Birmingham, AL, to celebrate its one-of-a-kind Grand Opening event accompanied by a ribbon-cutting ceremony and open house on Monday, Oct. 28, 2019, at 2500 Ensley 5 Points W Ave., Birmingham, AL 35218 from 6-9 PM.
iBoss Media - Oct 28, 2019
Regional Medical Group and Onyx Imaging Support Georgia Chiropractic Association's 107th Annual Fall Conference & Trade Show
Regional Medical Group and Onyx Imaging are two of the many to sponsor Georgia Chiropractic Association's 107th Annual Fall Conference & Trade Show. A 3-Day Event Featuring Medical Industry Professionals. Guests can register to attend at https://bit.ly/2IBiROS


Today U.S. Senator Herb Kohl's bill, the Prevent All Cigarette Trafficking (PACT) Act, was signed into law by President Barack Obama. The PACT Act cracks down on black market tobacco selling by closing loopholes in current tobacco trafficking laws, enhancing penalties for violations, and providing law enforcement with new tools to combat the innovative methods being used by cigarette traffickers to distribute their products. In 1998, the Bureau of Alcohol, Tobacco, Firearms and Explosives (BATFE) had six active tobacco smuggling investigations. Today there are more than 400 open cases.
"The cost of tobacco smuggling to Americans is not merely financial. Internet tobacco sales have been used by terrorist and organized crime groups to raise millions of dollars to support their illicit activities. This new law will help us ensure that we no longer continue to enable terrorist organizations to exploit the weaknesses in our tobacco laws to their advantage, allow states lose tax revenue, and provide children with easy access to tobacco products sold over the Internet," Kohl said.
Hezbollah, al Qaeda and Hamas have all generated significant revenue from the sale of counterfeit cigarettes. Hezbollah is estimated to have earned $1.5 million between 1996 and 2000 through tobacco smuggling. That money is often raised right here in the United States, and then funneled back to these international terrorist groups.
Kohl noted that cigarette trafficking, including the illegal sale of tobacco products over the Internet, costs states billions of dollars in lost tax revenue each year. It is estimated $5 billion of tax revenue is lost, at the federal and state level, each year. As lost tobacco tax revenue lines the pockets of criminals and terrorist groups, states are being forced to increase college tuition and restrict access to other programs because of these lost revenues.
The Internet represents a new obstacle to enforcement. Illegal tobacco vendors around the world evade detection by conducting transactions over the Internet, and then shipping their illegal products around the country to consumers. Just a few years ago, there were less than 100 vendors selling cigarettes online. Today, approximately 500 vendors sell illegal tobacco products over the Internet.
* Strengthen the reporting requirements for interstate cigarette sellers.
* Increase the criminal penalty from a misdemeanor to a felony and create a substantial civil penalty for violations, including violations of the reporting requirements and state tobacco tax laws.
* Grant federal and state law enforcement officials more powers to investigate and prosecute violators.
The PACT Act (S. 1147) was passed under unanimous consent by the Senate on March 11, 2010. On March 17, the House of Representatives passed identical legislation (H.R. 1676) by an overwhelming majority, 387 to 25.
Posted in: Cigarette Smuggling, Legislation.


As usual, anything nice I have is because my wife buys it for me :) Enter, the Petzval Lomography Art Lens. This is a FULLY manual lens. Not only is it manual focus, but it comes with 10 different aperture plates (3 of which are 'fun' shaped [see star shot below]) that you drop into the lens to change your aperture size and depth of field.
The lens itself is a beautiful piece or art. When I have it mounted to my Canon DSLR, it turns quite a few heads.


Originally called Horriford Wood, this is one of the oldest natural woods in existence in Britain, and is the 1000th Woodland Nature reserve. The woods and its surrounding area have been utilised by people for thousands of years. It lies to the North of, and partially surrounds, an Iron Age encampment known as Seaton Down Fort, where the remains of a bank and ditch can be seen.
Although some of the pine trees have been taken out...to allow for natural growth and extension of the deciduous trees...the woodland has been left to continue naturally, with no other planting by human means. Piles of logs from the felled pine trees have been left to provide a necessary habitat for insects and other small creatures; a source of food for woodland birds, such as Woodpeckers. Dead trees and fallen branches have been left for the same purpose, and also to provide a place of study of the natural evolution of woodlands.
This visit was in May 2010 when the woods were wall to wall with bluebells. Sadly, the photos haven't picked them out very well. It is such a lovely place for a wander even so. Very tangly and very old.
In the centre of the woods is an old reservoir, which is now private and used as a fishing pond. It was difficult to see through the tangly trees, and the glimpse I caught of it was covered in pond weeds. I did see a wader type of bird picking its way across the weeds, but it was too far away to identify it. It may have been a curlew.
On the eastern edge of the woods is Horriford Farm. The oldest parts date back to 1480, containing mullion windows, Elizabethan fireplace and an oak screen. To the left of the picture below is a very old pump house next to the stream.
More photos in the gallery album.


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redpajama_set_name: RedPajamaGithub


text:
Woodhull Raceway gearing up for 2016 Arnot Mall Car Show sponsored by Swarthout Recycling
Media Contact: Steven Ovens - woodhullracewaypr@gmail.com or (315) 729-3825 For Immediate Release - January 9th, 2016 Attachments: Woodhull Raceway Logo, Turn 5 Media photo, Press Release (Woodhull, N.Y.) - 'New York's Toughest Bullring' has had some of the toughest competition in the Northeast, featuring 370 Modifieds, Crate Sportsman Modifieds, 360 Late Models, Street Stocks, Mini Stocks, Front Wheel Drives and the Woodhull Warriors. All of these divisions will return for 2016 with the only potential changes expected to be for the Street Stocks pending several official and driver meetings. But before any laps are turned on the Steuben County third-mile oval, racers and fans can look forward to the annual Arnot Mall Car Show, which will be sponsored by Swarthout Recycling for the 7th year in a row. Woodhull's car show is one of the busiest weekends for the Arnot Mall, located directly off Interstate 86 in Big Flats, NY and the 2016 version expects to be no different. Swarthout Recycling is a well-known supporter of local motorsports located in Beaver Dams, NY. They specialize in scrap metals including mixed steel, aluminum, copper, brass and cast iron. The recycling department accepts cardboard, newspaper, mixed office paper and junk mail, clear and green glass, tin and plastic. Swarthout is also a race fan's go-to source for household and commercial refuse. Their large fleet of trucks and equipment has one of the area's largest assortments of roll-off canisters in various sizes. They can also provide front-loading trash dumpsters in 2, 4, 6, and 8 cubic yard sizes for commercial refuse. As if those services weren't enough, Swarthout Recycling also can provide demolition, long haul trucking and a state-of-the-art mobile document destruction vehicle for safe and secure shredding of delicate records and documents. The always-potent Woodhull racing community will line the halls of the Arnot Mall starting with move-in night on Friday March 18th as the mall closes business that evening. Saturday and Sunday will be the official car show with the raceway having a large display in center court. One change for 2016 will turn a lot of heads and spark the interest of the local race teams in attendance. For the first time in several years, Woodhull Raceway is proud to announce the Team Pit Stop Competition held in center court will return on Saturday evening, slated to begin at 6:30PM. Teams of 3 will be accepted featuring a jack man, tire carrier and tire changer, with crew members being allowed to enter the contest on only one team. The competition will feature changing a right rear tire in the fastest amount of time without leaving any lug nuts loose. Teams may register at the show OR by emailing the team name and team members to woodhullracewaypr@gmail.com. There is no entry fee to enter your race vehicle into the car show, but you must submit your entry by Friday March 11th, 2016. You may submit your registration to woodhullracewaypr@gmail.com, by sending a message to the Woodhull Raceway Facebook page, by calling Steve at (315) 729-3825 or by calling Brandi at (607) 857-1337. Woodhull Raceway Car Show Entry Information: Driver Name: Car Number: Track: Division: Chassis: Engine: 2015 Stats (optional):


Provides FoodShare to households that meet certain financial and non-financial requirements helping low-income families and individuals to buy nutritious food. For more information please call the Western Region for Economic Assistance (WREA) at 1-888-627-0430 or visit https://www.dhs.wisconsin.gov/foodshare/index.htm.
Provides health care benefits to individuals and families who meet certain financial, health, or age requirements. For more information please call the Western Region for Economic Assistance at 1-888-627-0430 or visit http://www.dhs.wisconsin.gov/medicaid/INDEX.HTM.
Online: visit ACCESS.wi.gov to complete an application.
Call: Western Region for Economic Assistance at 1-888-627-0430 to complete an application or schedule an appointment at your local agency.
Local Agency: Come to the Clark County Department of Social Services to complete a request for assistance and set the filing date. Once this request for assistance is received by the Western Region for Economic Assistance, the applicant will be contacted to set up an application interview.
A child care subsidy is provided to employed parents who meet program and income eligibility. Parents must use a regulated provider and receive an authorization for reimbursement. For more information please call the Western Region for Economic Assistance (WREA) at 1-888-627-0430 or visit http://dcf.wi.gov/childcare.
1. Online: visit ACCESS.wi.gov to complete an application.
2. Call: Western Region for Economic Assistance (WREA) at 1-888-627-0430 to request an application.
3. Local Agency: Come to the Clark County Department of Social Services to complete a request for assistance and set the filing date. Once this request for assistance is received by the Western Region for Economic Assistance, the applicant will be contacted to set up an application interview.
If you have questions regarding your FoodShare, Medical Assistance, or WisconsinShares benefits or you need to report a change, please contact the Western Region for Economic Assistance at 1-888-627-0430.
Changes that should be reported: Birth of a child, address changes, income or asset changes, people moving in or out of the household, expense changes, or child care authorization changes.
The Wisconsin Home Energy Assistance Program (WHEAP) provides assistance for heating costs, electric costs, and energy crisis situations. The WHEAP program heating season runs October 1 through May 15. For more information please contact the Clark County Department of Social Services at 715-743-5262.
To report suspected fraud of public assistance benefits (FoodShare, Medical Assistance, or Child Care Assistance) please call the Western Region for Economic Assistance at 1-888-627-0430.
For information on the Affordable Care Act and qualifying for health insurance through the Marketplace, please call 1-800-318-2596 or visit https://www.healthcare.gov.


10% Off everything even our sale events.
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Happiness is contagious so go ahead and give it to your friends and workmates.
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Q: i want to convert sound to numbers in audacity you can use sample data import which imports a .txt file with numbers in it and converts the numbers to a sound file. but I want to do the opposite I want to convert sound into numbers. is there a way to do that?

A: I believe the answer to your solution is here : http://manual.audacityteam.org/man/sample_data_export.html.
Defition:
Sample Data Export reads the values of successive samples from the selected audio and prints this data to a plain text, CSV or HTML file. Further information may be added as a "header" at the top of the file.
See also the companion tool Sample Data Import.

redpajama_set_name: RedPajamaStackExchange


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HUSQVARNA MOTORCYCLES CONGRATULATE ZACH OSBORNE ON A SUCCESSFUL RACING CAREER
THANK YOU, ZACH!
Wrapping up an illustrious career spanning over 16 years, Zach Osborne has announced his retirement from professional motocross and supercross racing. Over the last seven years, the 32-year-old has secured four major U.S. championships and countless triumphs with the Rockstar Energy Husqvarna Factory Racing Team and for that, Husqvarna Motorcycles would like to express a sincere thanks to Zach as he moves into his next chapter.
Known for his tenacity and never-give-up mentality, Osborne has established himself as a fan favorite over the years while amassing an impressive list of accomplishments together with Rockstar Energy Husqvarna Factory Racing. Beginning a tenacious run in 2017 aboard the FC 250, Osborne swept both the 250SX Eastern Championship and the AMA 250MX Championship in the same season before returning to successfully defend his 250SX Eastern title in 2018.
He stepped up to the premier 450 class in 2019 and he quickly hit his stride on the FC 450 ROCKSTAR EDITION, finishing on the podium seven times (six in motocross, one in supercross) during his rookie season. He went on to secure his first-career 450SX Main Event win at the Salt Lake City SX finale in 2020 and he set fire throughout the summer claiming the 450MX Championship in what would ultimately serve as his last full season of racing due to an ongoing back injury throughout 2021. Ending his career on a high note with plenty to be proud of, Husqvarna Motorcycles sends a big congratulations to Zach on a successful career.
Zach Osborne: "After 16 years of professional racing, the time has come for me to call it a career. I've tried everything in my power over the last six months to get my health back up to the standard it needs to be to race at the highest level and after just a few weeks of riding supercross at full intensity, I realized it just wasn't meant to be. I'm so grateful for the journey I've had as a professional. I've met so many incredible people and been a part of some of the finest organizations in motorsports. This was not an easy decision, or one I took lightly, but it was the right decision. I'm forever grateful to my family, fans and teams for their support throughout my time as a professional. In the next chapter, I want to focus my time more on giving back to those who have given to me."
Stephen Westfall – Rockstar Energy Husqvarna Factory Racing Team Manager: "I've had the pleasure of knowing Zach for a long time dating back to his amateur days and it's been awesome getting to work with him for the past seven years. Zach helped put Rockstar Energy Husqvarna Factory Racing on the map, winning four championships for the brand and being a good mentor for the younger riders. He has had a great career and we wish him all the best in his next adventure."
Robert Jonas – VP Motorsports Offroad: "Zach's achievements during his time with the team has really elevated the Husqvarna Motorcycles brand in the USA. He won four championships in AMA Supercross and Pro Motocross on both FC 250 and FC 450 machinery, and without a doubt he was at his very best during the seasons that he raced for us. His career was not a conventional one, but through hard work and dedication, he really emerged as one of the best racers in the world in recent years. On behalf of Husqvarna Motorcycles, I would like to congratulate Zach for everything that he has achieved with us and I wish him well for the future."
Osborne's pioneering roots actually began with the Austrian-based company more than 20 years ago as he launched his amateur motocross career with KTM in 1996. A young Osborne became the second-ever KTM Jr. Racing SX Champion in '98 before going on to headline the brand's minibike efforts on the new KTM 65SX. Following impressive results at the national level, Osborne became an instrumental part in developing the new-generation 85SX in the early 2000s, which has significantly impacted the bike's success over the last two decades.
He later took his talents overseas to compete in the FIM World Motocross Championship, where he collected 14-career FIM World Motocross Championship MX2 podiums, a British MX2 Championship and one-career FIM World Motocross win. He also represented the U.S. as a member of the prestigious Motocross of Nations (MXoN) team, as well as the World Trophy Team at the International Six Days Enduro (ISDE).
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Fully equipped engineering office, CAD and technical library, specialist software includes LR-SSC structural analysis and MAST4 stability calculations, comprehensive survey equipment includes utra-sonic, dye-pen, digital thermometers, pressure and airflow measurement.
Seatime Marine Consultants is a consortium of marine consultants with considerable deep sea and small vessel experience, looking to ease off as they approach retirement, but without losing or letting down their customers. By sharing workloads and "mentoring" the next generation, a win-win solution is provided for both consultant and customer whereby the consultants continue to receive an ongoing income from their own client base, whilst their customers availably of access to the experience and expertise the customers have come to know, require and respect. Authorised Code Examiners and Tonnage Measurement for <24m vessels. Inclining, stability, Full survey services, marine engineering and naval architecture. Specialists in propellers, marine gas turbines and ARM analaysis.
Older PostNewman Giles Paines & Co. Ltd.


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Torsten Hallman (Uppsala, 17 de outubro de 1939) é um ex-motociclista sueco, tetracampeão mundial de motocross.

Hallman foi um dos principais competidores de motocross durante os anos 1960, vencendo a categoria de 250cc do campeonato mundial em quatro oportunidades (1962, 1963, 1966 e 1967). Seu número de títulos apenas não foi maior por uma ferrenha disputa pelos títulos naqueles anos com o belga Joël Robert, chegando ao ponto de entre os anos de 1964 e 1968 apenas os dois alternarem entre os primeiro e segundo lugares — de fato, nas primeiras onze temporadas do campeonato, entre 1962 e 1972, além de Hallman e Robert, apenas o soviético Victor Arbekov conseguiu um título na categoria, em 1965. As disputas ainda hoje são consideradas uma das melhores e mais ferrenhas na história do campeonato.

Junto de Bill Nilsson, Rolf Tibblin e Sten Lundin, Hallman foi parte de um grupo de pilotos oriundos da Suécia que dominaram o motocross entre o final dos anos 1950 e o final dos anos 1960. Embora corresse nas 250cc, ao contrário de Nilsson, Tibblin e Lundin, que corriam nas 500cc, Hallman se sobressaiu com seus quatro títulos, com os outros três conquistando apenas dois cada.  Tendo sido contratado pela Yamaha em 1971 para desenvolver novas motocicletas, Hallman foi instrumental no desenvolvimento de um novo sistema de suspensão traseiro, onde era utilizado apenas um amortecedor, que se tornaria normativo nas motos pouco tempo depois, e ajudou seu conterrâneo Håkan Andersson a vencer a edição de 1973 do mundial das 250cc.

Após sua aposentadoria, ele começou a vender calças e luvas nas corridas para ajudar a complementar sua renda. Os produtos eram vendidos por catálogo durante os anos de 1970 e considerados inovativos, se tornando muito populares nos Estados Unidos. Eventualmente, ele criou a marca THOR Motocross (Torsten Hallman Original Racewear), crescendo ao ponto de se tornar uma das principais marcas de vestimenta dentro do motocross mundial. Isto, aliado ao seu sucesso no motocross, principalmente por suas disputas com Robert, tornou Hallman uma forte influência na introdução do motocross nos Estados Unidos, tendo sido reconhecido em 2000, quando foi introduzido no Motorcycle Hall of Fame da American Motorcyclist Association (AMA).

Motociclistas da Suécia
Naturais de Uppsala

redpajama_set_name: RedPajamaWikipedia


The Blue Silver and Enameled Bronze is an impactful, round, concave adjustable Ring made with Sterling Silver and Enameled Bronze. Its precious blue color takes us to the deep color of the Mediterranean open sea waters. You can combine it with the Blue Enameled Earrings and the Blue Donut Pendant of the same Enameled Jewels Collection. It has a diameter of 3.5 cm. Add a touch of bright color to your look and wear the Blue Silver and Enameled Bronze Ring!
The Blue Silver and Enameled Bronze Ring was handmade by Valentina Laganà, a Sicilian versatile artist based in her beloved Turin. As if writing her own diary, Valentina designs contemporary jewels with her unique personality, elegance and beauty.


This program is designed to educate and assist those residents of the Township of Bruce and the Village of Romeo.
The program includes 6 smoke alarms and 1 carbon monoxide detector per household. Requirements of the program include a home inspection, proper detector location, installation of detectors and education. If you are interested in participating in this program, please fill out the form below.
Please note: PROGRAM ENDS JULY 15TH, 2019.


Images are incredibly important in the rat race for attention on social media. Recent studies show that when people hear information, they're likely to remember only 10% of that information three days later. However, if a relevant image is paired with that same information, people retained 65% of the information three days later. According to Buffer Social, tweets that contain images get 150% more retweets than tweets that don't have images. Additionally, Buzzsumo reports that Facebook posts that contain images get 2.3 times more engagement than those with no images.
As an inbound marketing agency, a big part of our job is social media management. Social media marketing is important, and in today's modern world maximizing your online presence is a must.
How do you maximize your online presence?
In a nutshell, you must consistently engage with your market on the social media platforms they frequent. This includes posting relevant content that your audience actually wants to see, and one of the most important aspects of that is putting out visually appealing content.
First, you must analyze your target market and find out what kinds of content they want to see. What entertains them? What fuels their passions? What interests them outside of your company? All of these things must be carefully considered before developing your social media plan of attack. Once you know the types of material and content that would be most productive for you to post, you should think about the best way to draw attention to them. The best way to draw attention to many things – social media included – is through visual stimulation.
Simply put, if you want people to notice your posts, you need to make them notice those posts via relevant accompanying visuals.
What will these visuals look like?
Different markets look for different things. The same things that will attract some customers will repel others – and that's okay. Not everyone is your ideal client, and you can't make everybody happy. Focus on what your specific target market wants to see, and produce that content. Sometimes, it will take the form of an infographic. According to MassPlanner, Infographics are "liked" and shared on social media 3 times more than any other type of content! Or maybe, it's an awesome photograph. Or perhaps a graphic, video, or gif. The type of visual content you're posting should be different depending on the social media platform you're on. For instance, Snapchat is better for posting behind the scenes, real-time shots of your products and office, and Instagram is ideal for posting images of the face of your brand.
Adding visual emphasis in your social posts might be easier than you think: hand-drawn graphics aren't necessary for every single post. Simply putting text on an image boosts both visibility and interest. Our social media team developed a social media series centered around weird Texas laws for an online legal service, TexasLegalDocs. It was a great way to show off the brand's personality while posting content that was both relevant and interesting to the brand's audience.
Studies show that when the title of a blog post is in an image accompanying the post, the open-rate increases. The image below was used as an attention-grabber to direct traffic to a blog post about long term care for a financial planning organization we worked with. Statistically speaking, people like statistics, and putting one on an image can be a great way to get noticed.
Wendy's does a fabulous job of managing their social media pages. In the post below, they've taken the most boiled down version of their offer possible and splattered it across an image with attention-grabbing color contrasts and mouth watering images. Someone scrolling through their Facebook feed couldn't possibly ignore the point of the post, because it's so delightfully simple and bright. If Wendy's had written the exact same thing and put it in the text box rather than on an image, most people scrolling through their Facebook feed would probably never notice it.
Developing quality visuals for your social media plan can be challenging. Remember, quality is better than quantity in this case. It's better to have fewer, more powerful posts than to damage your online reputation and lose followers over too many low-quality posts. Making sure your visuals are appealing and not just "noise" is just as important as finding the right medium to express them.
Managing a productive and successful social media presence is just one part of inbound marketing. Inbound changes the way that people see businesses, and it changes the way that businesses interact with and reach out to their customers. If you're interested in learning more about the proven power of inbound, download our free checklist today: How to Run an Inbound Marketing Campaign.


Device to study the response of stem cells in culture, which simulates the blood flow from the point of view of stress (pressure) and time history (heart beat).
Device ease of use: easy replacement of culture plate, compact size.
From functional diagram up to prototype realisation.
Development of a turnkey device (including control system and user control interface).
Device reproducing the set of motion profiles in a very accurate way.
The mechanical design not only ensures functionality but also facilitates management: its layout ebables to easily replace the cultures to be tested; in addition, its compact dimensions guarantee its use inside standard size incubators.


Oh Yes! Samsung publicized Galaxy Note Edge at Rs. 64,900 only. Curved side screen which was displayed in company with the Galaxy Note 4 in 2014 event. It'll be available into picked retailers for Rs. 64,900.
As i said before it contains a curved display, named Edge Screen which you seek on the right side. It enables quick navigation for accessing apps, alerts and others systems – doesn't matter whether it covered up or closed.
You can create shortcut menu for sides and turn it into one touch input or reminder. Company featured a virtual desktop similar to working place which you can manage from side otherwise operate from home or app drawer.
Samsung has managed to pack in virtual desktop-like working environments which can be switched using the side display or you could also navigate the home screen or app drawer using this edge.It also has the Samsung S Pen just like we had seen in the Note 4.
You can arrange screen by your favorite personality , pictures, tastes etc. Also you can write texts buy utilizing S pen like Note 4.
Samsung Galaxy Note Edge launched at Rs. 64990. It brought stylish display but it has reported hectic for lefties. Apart from that it's looking superb but is it worthy to upgrade from previous Note 4 or should you pick it as a next handset?
Also iPhone 6 and l plus is in same price range and other brands too. Do you buy iPhone or android smartphone with almost similar cost. Choice is yours. Otherwise Samsung Galaxy Note Edge specs are very well. Overall I can say you can try or buy if you prefer specs with this price. But still if you have an issue for buying your smartphone then let us know. We are ready always to help you anytime with our best.


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EU regulators wrangle over Twitter data privacy penalty
by Kelvin Chan
This April 26, 2017, file photo shows the Twitter app icon on a mobile phone in Philadelphia. European Union privacy regulators are wrangling over the penalty Ireland's data privacy watchdog was set to issue Twitter for a data breach. The Irish Data Privacy Commission was expected to issue its decision in the Twitter case, which would be its first involving a U.S. technology company since the new privacy law, known as GDPR, took effect in 2018, allowing for hefty fines. But it said Thursday, Aug. 20, 2020 that its counterparts in other countries - so-called concerned supervisory authorities - challenged a draft decision it circulated in May. (AP Photo/Matt Rourke, File)
European Union privacy regulators are wrangling over the penalty Ireland's data privacy watchdog was set to issue Twitter for a data breach, pushing back the case's long awaited conclusion under the bloc's tough new data privacy rules.
The Irish Data Privacy Commission was expected to issue its decision in the Twitter case, which would be its first involving a U.S. technology company since the new privacy law, known as GDPR, took effect in 2018, allowing for hefty fines.
But it said Thursday that its counterparts in other countries - so-called concerned supervisory authorities - challenged a draft decision it circulated in May.
"A number of objections were raised," the Irish regulator said in a brief statement. "However, following consultation a number of objections were maintained and the (Irish Data Privacy Commission) has now referred the matter to the European Data Protection Board," the independent body representing the bloc's privacy regulators. It provided no other details. The board has up to two and a half months to come up with a decision.
Under the EU's General Data Protection Regulation, a single regulator takes the lead role in cross-border data privacy cases as part of a 'one-stop shop' system.
Twitter and other U.S. tech companies like Apple, Facebook and Google have their European headquarters in Dublin, making the Irish watchdog their lead privacy regulator in the EU.
But in this system, the main regulator has to share its draft decision with regulators in other EU member states and take their feedback into consideration. The Twitter case could foreshadow more disagreements and delays that Irish authorities may face as they wrap up about two dozen other investigations involving the Silicon Valley giants.
The Twitter case stems from a security breach that affected its Android app users and let anyone view protected tweets over more than four years. The Irish regulator said in a June report it was investigating the company for failure to report the breach within 72 hours.
Under GDPR, companies that don't make such timely disclosures can be fined up to 10 million euros ($12 million) or 2% of a company's annual revenue, whichever is higher. In 2019 Twitter's revenue reached $3.46 billion, making a potential fine worth up to $69 million.
Irish regulator investigates Facebook over exposed passwords
© 2020 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed without permission.
Citation: EU regulators wrangle over Twitter data privacy penalty (2020, August 20) retrieved 18 January 2021 from https://techxplore.com/news/2020-08-eu-wrangle-twitter-privacy-penalty.html
Evolvable neural units that can mimic the brain's synaptic plasticity
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Google releases Blob Opera just in time for the holidays
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Interesting article by John Dorney on the syndicalist tactic of the general strike and its relationship with the struggle for Irish independence in the early 20th century.
Article by John Dorney telling the story of the Special Infantry Corps, a military unit set up during the civil war of 1922-3 to suppress agrarian agitation and strikes.
A short history of Ireland's most significant industrial dispute: the mass lockout of 20,000 workers by 400 employers in Dublin from August 1913 to January 1914.
An account of the Barcelona bus workers victory.
A critique of trade and syndicalist unions from a communist perspective by G. Munis.


I just got a new job and i will be travelling for work to DRC and zambia. I will have transport and local support ( translator, locals, etc). But from experianced people here what can one expect? And what is must see places?
Where abouts in Zambia and DRC? they are both very big countries.
DRC, I am going to Kinshasha.
Zambia is places like chililabombwe, Lusaka and most of Zambia.
Kinshasa is a bit of a hole. Don't go for a walk after dark. French is Linga Franca, so interpreter is a must. I visited Kinshasa many times, usually in transit to other places, and I didn't like it at all. Dirty, and I felt really unsafe. I once saw some cops shoot a guy on the side of the street with their AK's. Happened on road between airport and hotel. Told driver to go like blazes!
Hotels charge in US$, and they are not shy to charge. Easy pay $300 for a night in a really shoddy hotel. And food isn't cheap either, unless you eat from the local places.
The Congo river has some cruises that you can go on, and the fishing isn't too bad if you are a bit away from the city. Wildlife is virtually non-existent, all been killed in poaching during civil war. You can't get very far from Lusaka, mainly because roads are so bad. Flying is pretty much only way to get around, but some of the local "airlines" are dodge to say the least. I remember a couple of years ago one crashed because a crocodile got loose from some guy's baggage! I actually flew with the pilot that died in that crash.
Zambia... so much to do and see there! Lusaka is lekker, there are malls that have all the usual SA shops, and some of the fast food outlets too. Rhapsody's has good food.
West of Lusaka, about a 2-3 hour drive is the Kafue National park, I've seen lion and ellies there, as well as all the lesser antelope etc. About another 3 hours west is Mongu, on the Zambezi. Steeped in history and tradition. Great fishing in the Zambezi for tigers. Head south of Mongu for some excellent tiger lodges etc.
East of Lusaka, more parks, also north-east.
South of Lusaka, a couple of hours drive is Kariba. House-boats heaven! Fishing, birding, game watching. Drink lots of beer to stay hydrated! Mosi lager is good!
About 5 hours south west of Lusaka are the Vic Falls, they speak for themselves.
Driving in Zambia is fine, just lots of police roadblocks abnd check-points. Your SA drivers licence is accepted (SADC). But if you have a prang you are guilty, end of story. So a local driver is a good thing to have. Then you can enjoy even more beers!
Seems Zambia is worth while exploring....so bring on my first trip!
I can put you in contact with South Africans all over the Southern Part of Zambia. Especially at Sinazongwe Near Kariba. The pic below is where you could stay - 50m from water when Kariba is full.
I am based in Lusaka.
Everything everyone here said about Zambia is correct, it is a great place!


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Juventus stepping up interest for Ajax winger Antony
Image Credits: Soccrates/Getty Images
Juventus are eyeing several targets in the summer in order to find a possible replacement for star forward Paulo Dybala.
Dybala's contract expires at the end of the season, and his deal will not be extended, leaving Massimiliano Allegri to find a replacement for his side.
Juve have been increasingly linked with moves for the likes of Angel Di Maria and Nicolo Zaniolo, with the two players set for moves from Paris Saint-Germain and AS Roma respectively.
Despite this, a report from Calciomercato has claimed that Ajax star winger Antony has also emerged as a target, with Juve having a serious interest in the Brazilian.
Antony has had a brilliant season with Ajax, scoring 12 goals and 10 assists in 33 games in all competitions, and with Erik ten Hag joining Manchester United, the Brazilian could be on his way out of Ajax.
The report adds that the Bianconeri have intensified their efforts to sign him over the last few weeks, with a possible move for him being one to keep an eye on.
However, the two clubs are not agreeing on his market value, with Ajax asking for at least €35 million, while Juve are not prepared to offer that much.
Other reports have indicated that Juve have plenty of competition for him, especially from Ten Hag's new club Manchester United, with the Brazilian possibly set to follow his manager to Old Trafford.
A report from Yoonis Mohamed claims that the United-bound manager has already spoken to Antony and Jurrien Timber over possible moves, with the Brazilian being ready to make his next step and leave the Dutch club this summer.
However, it also adds that nothing is advanced, and so Juventus are definitely still in the race.
The Brazilian's future is in serious doubt, with him set to be the latest name in a long list of notable Ajax departures over the years.