text:
Viscount Wimborne, of Canford Magna in the County of Dorset, is a title in the Peerage of the United Kingdom.

History
The title was created in 1918 for Ivor Guest, 2nd Baron Wimborne. The Guest family descends from the engineer and businessman John Josiah Guest. On 14 August 1838, he was created a baronet, of Dowlais in the County of Glamorgan, in the Baronetage of the United Kingdom. He was succeeded by his eldest son, the second Baronet. In 1880, he was created Baron Wimborne, of Canford Magna in the County of Dorset, in the Peerage of the United Kingdom. On his death, the titles passed to his eldest son, the second Baron. In 1910, four years before he succeeded his father, he had been raised to the Peerage of the United Kingdom in his own right as Baron Ashby St Ledgers, of Ashby St Ledgers in the County of Northampton. Upon his retirement as Lord Lieutenant of Ireland in 1918, he was further honoured when he was made Viscount Wimborne, of Canford Magna in the County of Dorset, in the Peerage of the United Kingdom. His son, the second Viscount, represented Breconshire in the House of Commons. , the titles are held by the latter's grandson, the fourth Viscount, who succeeded his father in 1993.

Several other members of the Guest family have also gained distinction. Montague Guest, third son of the first Baronet, was a Liberal Member of Parliament. Frederick Edward Guest, Henry Guest and Oscar Guest, younger sons of the first Baron, were all prominent politicians. Also, Lady Charlotte Guest was the second wife of the first Baronet.

In 1867, the first Baron bought a large house at 22 Arlington Street in London, which remained the family's London residence until 1947.

Guest baronets, of Dowlais (1838)
Sir John Josiah Guest, 1st Baronet (1785–1852)
Sir Ivor Bertie Guest, 2nd Baronet (1835–1914) (created Baron Wimborne in 1880)

Barons Wimborne (1880)

Ivor Bertie Guest, 1st Baron Wimborne (1835–1914)
Ivor Churchill Guest, 2nd Baron Wimborne (1873–1939) (created Baron Ashby St Ledgers in 1910; created Viscount Wimborne in 1918)

Viscounts Wimborne (1918)

Ivor Churchill Guest, 1st Viscount Wimborne (1873–1939)
Ivor Grosvenor Guest, 2nd Viscount Wimborne (1903–1967)
Ivor Fox-Strangways Guest, 3rd Viscount Wimborne (1939–1993)
Ivor Mervyn Vigors Guest, 4th Viscount Wimborne (born 1968)

The heir apparent is the present holder's son, the Hon. Ivor N.G.I. Guest (born 2016).

References

Kidd, Charles, Williamson, David (editors). Debrett's Peerage and Baronetage (1990 edition). New York: St Martin's Press, 1990,

Viscountcies in the Peerage of the United Kingdom
Noble titles created in 1918
Noble titles created for UK MPs

redpajama_set_name: RedPajamaWikipedia


← You CAN Take it With You!
It's been a while since the excitement of the 4o Book Challenge began. And I HATE to say that that excitement may have weaned a little bit. Remember back when I told my class about it, and everyone was really energized by it? Ready to do it and not at all worried? And remember how my friend Brittany asked if I would do it, too, and I begrudgingly gladly accepted? Yes? Well let me update you on how it's going.
First of all, I feel like I should share with you what my kiddos are saying about it. Of course, as with any important thing in our class, it becomes a topic on our blog. I'm excited to say that the topic has come up multiple times in the "What I liked…" section of their notes for student-led conferences (yes, that is a topic I'm going to add here soon!), and that many have WAY over half of their challenge done already!
Requirements for the 40 Book Challenge, which is inspired by Donalyn Miller's The Book Whisperer.
Not surprisingly (at least to me), most kiddos started with what they know and what they love: fiction. Many of them knocked out Realistic Fiction first, then did their chapter book choice, and then tried mystery before they got a little annoyed by my list. Still, they trudged on, heading towards informational and poetry. I was noticing, though, that there has been very little traditional literature or biography/autobiography/memoir showing up in the hands of my readers lately (more on that later).
What? You want to know how I'm doing with the 40 Book Challenge? Me? Well….
I'm gonna be really honest with you that I have not been doing my part to keep up with the 40 Book Challenge like I'd hoped and like I'd expected. I think I am probably at 5 or 6. I know, right??? YUCK! I have had very good intentions, and I truly believe in the importance of showing my reading life to my students, but like I mentioned earlier, I'm having a hard time finding prioritizing time to make it happen. There always seems to be something else to do, you know?! But I WANT to make it happen (I really feel like I'm letting my friends down!), and since I don't make resolutions, I guess it's time to make a goal and a plan to achieve it. And I'd love your help!
Posted on January 29, 2014 by Jen Bearden	• This entry was posted in Classroom, Reading and tagged 40 Book Challenge, books, reading, time, torn. Bookmark the permalink.
I'm way behind as well, although I tried to keep up with my Mock Newbery Club and my Mark Twain Breakfast Club. I suspect if I had time to read Donalyn Miller's Reading in the Wild, I might find a way to salvage my reading year. I loved her first book, The Book Whisperer.
I'm way behind with my reading as well, although I did try to keep up with my Mock Newbery Club reading and my Mark Twain Breakfast Club. I suspect that if I could squeeze it in, I need to read Donalyn Miller's Reading in the Wild. I got so much out of her first book.
I take time each night to read at least 15 minutes. My two are in bed, my wife on the computer and my iPhone turned to do not disturb. This allows me to get into the book each night. Plus, it unplugs me from the outside world.


text:
'Simon created a world where everyone wants to get rich quick' says Cowell's brother Nicholas
Updated: 14:00 EST, 26 January 2012
Simon Cowell's brother Nicholas has told how the X Factor and Britain's Got Talent creator changed the world by contributing to a culture where 'everyone wants to get rich quick'.
The 50-year-old property developer - two years Simon's junior - praised his brother's 'unbelievable' achievement and revealed that he 'works hard'.
Nicholas bought his first property when he was 20 and his company, The Estate Office, recently paid £17 million for the 70-room, five-star Verta hotel and spa in Battersea.
'He changed the world': Simon Cowell (pictured this week in Blackpool) contributed to a culture 'where everyone wants to get rich quick' according to his brother
In an interview with ES Magazine, out tomorrow, he said: 'These days, partly due to my brother, everyone wants to get rich quick.
'The world is a different place from when we were growing up. There was never this thought that you had to be successful or make millions of pounds to be happy.'
Nicholas, who lives in a £2.5 million house near Chelsea with his wife Katie and their two children, Georgia, seven, and Harrison, five, added: 'I wouldn't compare my success with his. He is very successful. I'm okay.'
Sibling rivalry: Nicholas, pictured with brother in 2004, says 'He is very successful. I'm okay'
As The X Factor was named best talent show at last night's National Television Awards, Britain's Got Talent presenter Declan Donnelly warned wannabe stars that Simon Cowell rejoining the judging panel this year - and will be redoubling his efforts to terrify the acts to boost audiences.
And the winner for the best Twitter picture goes to... The National Television Awards through the eyes of the... Amanda Holden's three-day fight for life: Mum given emergency blood tranfusions after giving birth prematurely...
How Simon Cowell built a £200m fortune
Last year the music mogul left both shows and The X Factor was beaten in the ratings by BBC rival Strictly Come Dancing. But Donnelly, who co-hosts Britain's Got Talent with Ant McPartlin, said: 'Simon is back with a renewed energy.
'He is being extra hard on the acts. Not just the rubbish ones, but those who are pretty good but not quiet up to scratch. He's just waving his hand and saying, "We're looking for a world-class act, and you're just not good enough". He's definitely being meaner.'
Stepping into the spotlight: The full interview appears in ES magazine, out tomorrow
Simon Cowell changed the world, says his brother Nicholas
Ten people are killed at Orthodox Christian festival when seating collapses at event in Ethiopia, leaving...
Iran-backed Houthi rebels slaughter 116 Yemeni troops in weekend missile strike on barracks mosque before...
The Queen 'considered stripping Harry and Meghan of Sussex titles and HRH but feared looking "petty"': New...
PIERS MORGAN: Spare me your 'patriotic' crocodile tears, Harry - you DIDN'T have to quit. You chose to ditch the Queen, the monarchy, your military comrades and your country… to become a royal Kardashian and keep Meghan happy
The Queen 'considered stripping Harry and Meghan of Sussex titles and HRH but feared looking "petty"': New details of Megxit deal emerge as Duke has private 'catch-up' with Boris Johnson before heading to Canada

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}

Perturbative predictions about quantum-electrodynamic phenomena implied by a QED Lagrangian can be computed using the Feynman rules, a regularization method to circumvent ultraviolet divergencies, and a renormalization scheme. Regularization method results in regularized n-point Green functions; a suitable limiting procedure (a renormalization scheme) then leads to physically sensible predictions that are independent of the particular regularization method used. But no known regularized n-point Green functions can be regarded as being based on a physically plausible theory of quantum-electrodynamic phenomena since the derivation of each disregards some of the basic tenets of conventional physics (e.g., by lacking a Lagrangian, by not being Lorentz-invariant, by introducing particles with wrong metric or statistics\ldots). \it So the perturbative predictions of QED presently cannot be derived from a physically plausible theory\rm; for a history of, and comments on this basic problem see, e.g.,\cite{Cao}. Dirac\cite{Dirac} believed that removal of this conceptual inconsistency may lead to an important advance in field theories.

To show that one can remove this inconsistency \it already in four-dimensional space-time, \rm we will introduce a new, physically motivated modification of the QED Lagrangian and consider it within the theoretical framework of 't Hooft and Veltman\cite{Hooft}: They avoid canonical formalism and take diagrams as the basis from which everything must be derived; so they give a perturbative definition of the S-matrix directly in terms of diagrams corresponding to a given Lagrangian as specified by \it postulated \rm Feynman rules. The question is: How do we modify the QED Lagrangian so that the resulting regularized S-matrix is derived from a theory that is physically plausible?

Gupta\cite{Gupta} has shown already in 1952 that one can modify the QED Lagrangian so that the new Lagrangian results in the S-matrix of QED regularized by certain Pauli-Villars method. And twenty years later 't Hooft and Veltman\cite{Hooft} introduced the method of unitary regulators (HV-method) that (i)~is a variant of Pauli-Villars methods for regularizing propagators, (ii)~requires only an exceedingly simple modification of the initial Lagrangian, and (iii)~is very suitable for proving the causality of the regularized $n$-point Green functions and the unitarity of the resulting S-matrix. Unfortunately both methods introduce also unphysical particles with wrong metric or statistics. To get rid of this serious conceptual deficiency, we will generalize the HV-method.

We will demonstrate the utility of the generalized HV-method by using it to show that there is a perturbative S-matrix of quantum-electrodynamic phenomena derived from a theory that is \it physically plausible \rm(a pp-theory, for short) \it in the following sense: \rm
\begin{itemize}
\item[(i)]A pp-theory of quantum-electrodynamic phenomena is specified in a continuous, four-dimensional space-time by a local, Lorentz-invariant, physically motivated modification of a QED Lagrangian.
\item[(ii)]The Feynman rules for this modified Lagrangian, \it defined \rm as specified by 't Hooft and Veltman\cite{Hooft}, result in Feynman diagrams that are finite and equal the diagrams of QED but with regularized propagators.
\item[(iii)]All constants of a pp-theory are measurable in principle; \it there are no auxiliary parameters. \rm
\item[(iv)]For certain values of these constants, the QED propagators are the same kind of low-energy approximations to their regularizations as required for renormalization by Bogoliubov and Shirkov\cite{Bogol} in certain variants of the Pauli-Villars method.
\item[(v)]The n-point Green functions of a pp-theory, \it defined \rm as specified by 't Hooft and Veltman\cite{Hooft} in terms of Feynman diagrams, are causal.
\item[(vi)]The perturbative S-matrix of a pp-theory, \it defined \rm as specified by 't Hooft and Veltman\cite{Hooft} in terms of n-point Green functions, is unitary, Lorentz-invariant, charge and total four-momentum conserving, and relates \it only physical electrons, positrons and photons. \rm
\end{itemize}
Such a pp-theory of quantum-electrodynamic phenomena is not yet known; we cannot incorporate a finite-cutoff, Pauli-Villars, dimensional, or lattice regularization of QED in a pp-theory.

\section{Lorentz-invariant regulators without singularities}

As in the HV-method to each additional singularity of a regularized Feynman propagator corresponds an additional particle\cite{Hooft}, we will first show how we can Lorentz-invariantly regularize Feynman propagators so that they do not acquire additional singularities and have the K\"all\'en-Lehman representation used in proving causality and unitarity\cite{Hooft,Veltm}. Regarding metric and other conventions we follow Refs.~\onlinecite{Hooft,Veltm}; in particular, a four-vector $k = (\vec{k}, ik^0)$, and $k^2 \equiv \vec{k}\cdot \vec{k} - (k^0)^2$.

Consider a Lorentz-invariantly regularized spin 0 Feynman propagator, say, $\Delta_F(x)$ whose space-time Fourier transform
\begin{equation}
   (2\pi)^4 i\Four{\prop}(k) = (k^2 + m^2 - i\epsilon)^{-1}
      + \varphi(k^2 - i\epsilon)
   \label{scpro}
\end{equation}
where: (a)~the regulator $\varphi(z)$ is an analytic function of complex variable $z$ with a finite discontinuity somewhere across the negative real axis; (b)~$|(z+m^2)^{-1} + \varphi(z)| < A |z|^{-r}$ for $|z| > 2m^2$, with $r > 1$; (c)~$\varphi(z)$ is real if $\Re z > 0$ and $\Im z = 0$; (d)~$\varphi(z)$ depends on some constant $\Lambda$ so that for any $\Lambda \ge \Lambda_0 > 0$ it has properties (a) to (c) with $A$ independent of $\Lambda$, and, as $\Lambda \to \infty$,
\begin{equation}
   \sup_{\Re z \ge 0, \Im z = 0} |\varphi(z)| \to 0
   \quad\hbox{and}\quad
   \sup_{|z| < z_0} |\varphi(z)| \to 0
   \qquad\hbox{for any}\quad z_0 > 0 \,.
   \label{regpr}
\end{equation}
As a consequence, the spin 0 propagator provides such a low-energy approximation to its regularization (\ref{scpro}) as required for renormalization by Bogoliubov and Shirkov\cite{Bogol} in certain variants of the Pauli-Villars method.

Using Cauchy's integral formula we can conclude that the Lorentz-invariant regularization (\ref{scpro}) of the spin 0 Feynman propagator admits the K\"all\'en-Lehman representation
\begin{equation}
   (2\pi)^4 i \Four{\prop}(k) = \int_0^\infty {\rho(s)\over k^2
       + s - i\epsilon}\, ds
   \label{KLrep}
\end{equation}
with
\begin{equation}
   \rho(s) = \delta(s-m^2) + (2\pi i)^{-1} \lim_{y \to 0} [
      \varphi(-s-iy) - \varphi(-s+iy) ] \,,
   \label{KLrho}
\end{equation}
$s, y > 0$. Note that $\rho(s)$ is real, $\rho(s) = O(s^{-r})$ as $s \to \infty$, and
\begin{equation}
   \int_0^\infty s^m \rho(s)\, ds = 0
   \qquad\hbox{for}\quad m = 0, 1,\ldots < r-1 \,.
   \label{KLcon}
\end{equation}
So we can decompose the regularized spin 0 propagator $\Delta_F(x)$ into positive and negative energy parts: $\Delta_F(x) = \Theta(x_0) \Delta^+(x) + \Theta(-x_0) \Delta^-(x)$\cite{Hooft}.

The function $-i (2\pi)^{-4} ( \sqrt{\Lambda^2 - m^2} + \Lambda)^n (k^2 + m^2 - i\epsilon)^{-1} (\sqrt{k^2 + \Lambda^2 - i\epsilon} + \Lambda )^{-n}$, $\Lambda > m$, $n = 1, 2, \ldots $, is an example of a Lorentz-invariantly regularized spin 0 Feynman propagator that satisfies the above conditions with $r = n/2 + 1$. Unfortunately, we cannot use such propagators for a physically plausible regularization of QED since we do not know how to construct the corresponding \it local, \rm Lorentz-invariant Lagrangians.

A regulator that satisfies conditions (a)-(c) is by (\ref{KLrep}) a generalization of the Pauli-Villars regulator that has a continuous mass spectrum. Thus, to use such regulators to construct a pp-theory, we have to extend the 't Hooft-Veltman construction of Lagrangians in HV-method\cite{Hooft} to an \it infinite number \rm of additional fields. To provide an example of how this can be done, we will present a local, Lorentz-invariant Lagrangian whose propagators for \it interacting \rm fields can be taken as spin 1 and spin $1\over 2$ propagators regularized so that they acquire no additional singularities and have the K\"all\'en-Lehman representation.

\section{Lagrangian that regularizes QED propagators}

Following Veltman \cite{Veltm}, we will consider QED with massive photons in unitary gauge. Its Lagrangian reads
\begin{equation}
   {\cal L}_{{\scriptscriptstyle{\rm QED}}} = -{\textstyle{1\over 4}} (\partial_\mu A_\nu - \partial_\nu A_\mu)^2 - {\textstyle{1\over 2}} \mu^2 A^2 -
	\ab{\psi} (\gamma^\mu \ldp_\mu + m )\psi + ie \ab{\psi} \gamma^\mu\psi A_\mu + A_\mu J_\mu + \ab{J_e}\psi
        + \ab{\psi}J_e\,,
   \label{QEDL}
\end{equation}
where $J_\mu(x)$, $\ab{J_e}(x)$, and $J_e(x)$ are four-vector and bispinor source fields, and the non-vanishing photon mass $\mu < 2 \times 10^{-16}$ eV \cite{Parti}. The Feynman propagators for the four-vector field $A_\mu(x)$ and for the bispinor field $\psi(x)$ are:
\begin{equation}
   -i (2\pi)^{-4} { \delta_{\mu\nu} + \mu^{-2} k_\mu k_\nu
	\over k^2 + \mu^2 - i\epsilon } \,,\qquad
   -i (2\pi)^{-4} { -i \gamma^\mu k_\mu + m \over k^2 + m^2
	- i\epsilon } \,.
   \label{PDeq}
\end{equation}
We could use ${\cal L}_{{\scriptscriptstyle{\rm QED}}}$ to define a pp-theory as specified in Section~I, were the propagators (\ref{PDeq}) faster decreasing when $k^2$ tends to infinity.

However, one can modify the QED Lagrangian (\ref{QEDL}) so that the propagators for the fields $A_\mu$ and $\psi$ are such regularizations of propagators (\ref{PDeq}) that have no additional singularities. Take, for \it example, \rm the following real-valued, local, Lorentz-invariant Lagrangian:
\begin{mathletters}
\label{TTL}
\begin{equation}
   {\cal L}_{{\scriptscriptstyle{\rm TR}}} = - {\cal L}_1 - {\cal L}_{{\scriptscriptstyle{1/2}}} + ie\ab{\psi} \gamma^\mu \psi A_\mu
         + A_\mu J_\mu + \ab{J_e}\psi + \ab{\psi}J_e
   \label{TTLdf}
\end{equation}
with
\begin{eqnarray}
   {\cal L}_1 &\equiv& q_1^{-1} \int d^4p\, \Psi_\mu'(x,-p)
      [ \Lambda t(p^2) + p^\nu \ldp_\nu ] \Psi^\mu(x,p)
      \nonumber\\
   &&\qquad{}+ q_1^{-1} s_1 \int d^4p\, d^4p'\, f({p'}^2) f(p^2)
      [ \Psi_\mu'(x, -p')\Psi^{\prime\mu}(x,p) + p'_\nu p^\nu \Psi_\mu
        (x,-p') \Psi^\mu(x,p)
      \nonumber\\
   &&\qquad\quad{}- p^\mu \Psi_\mu(x,-p') {p'}^\nu \Psi_\nu(x,p) ] \,,
      \label{vecL}\\
   {\cal L}_{{\scriptscriptstyle{1/2}}} &\equiv& q_{{\scriptscriptstyle{1/2}}}^{-1} \int d^4p\, \ab{\Psi}_{{\scriptscriptstyle{1/2}}}(x,-p)
      [ \Lambda t(p^2) + p^\mu\ldp_\mu ] \Psi_{{\scriptscriptstyle{1/2}}}(x,p)
      \nonumber\\
      &&\qquad{}- q_{{\scriptscriptstyle{1/2}}}^{-1} s_{{\scriptscriptstyle{1/2}}} \int d^4p'\, d^4p\, f({p'}^2)
        f(p^2) [ \ab{\Psi}_{{\scriptscriptstyle{1/2}}}(x,-p') \gamma^\mu \Psi_{{\scriptscriptstyle{1/2}}}(x,p) p_\mu
         + {\rm c.c.} ] \,,
   \label{spinL}
\end{eqnarray}
\begin{equation}
   A_\mu(x) \equiv \int d^4p f(p^2) \Psi_\mu(x,p) \,,\qquad
   \psi(x) \equiv \int d^4p f(p^2) \Psi_{{\scriptscriptstyle{1/2}}}(x,p) \,,
   \label{macvar}
\end{equation}
\end{mathletters}
where: $\Psi_\mu(x,p)$ and $\Psi_\mu'(x,p)$ are four-vector-valued functions of two four-vectors $x$ and $p$; $\Psi_{{\scriptscriptstyle{1/2}}}(x,p)$ is a bispinor-valued function of $x$ and $p$; $2 a \ldp_\mu b \equiv a (\partial_\mu b ) - (\partial_\mu a) b $; $\ab{\Psi}_{{\scriptscriptstyle{1/2}}} \equiv \Psi_{{\scriptscriptstyle{1/2}}}^\dagger \gamma^4$; $t(p^2)$ and $f(p^2)$ are real-valued functions of real $p^2$, $\int d^4 p f^2(p^2) = 1$; $q_1$, $s_1$, $q_{{\scriptscriptstyle{1/2}}}$, $s_{{\scriptscriptstyle{1/2}}}$, and $\Lambda$ are real constants.

There are three kinds of reasons for the chosen form (\ref{TTL}) of the Lagrangian ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$:
\begin{itemize}
\item[(A)]It is our purpose to show that there are Lagrangians that generalize the t'Hooft and Veltman method of unitary regulators \cite{Hooft} to an infinite number of additional fields \it but do not introduce additional particles. \rm So we constructed the Lagrangian ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ modifying ${\cal L}_{{\scriptscriptstyle{\rm QED}}}$ on the analogy of HV-method\cite{Hooft}: (i)~We introduced an infinite number of four-vector and bispinor fields of $x$ that have a continuous index $p$, namely $\Psi_\mu(x,p)$, $\Psi'_\mu(x,p)$, and $\Psi_{{\scriptscriptstyle{1/2}}}(x,p)$. (ii)~We replaced the free part of ${\cal L}_{{\scriptscriptstyle{\rm QED}}}$ with the free Lagrangian of these fields,  $-{\cal L}_1 - {\cal L}_{{\scriptscriptstyle{1/2}}}$, which is of the first order in $\partial$ and has a nondiagonal mass matrix. (iii)~In the interaction and source terms of ${\cal L}_{{\scriptscriptstyle{\rm QED}}}$, we replaced the fields $A_\mu(x)$ and $\psi(x)$ with weighted integrals (\ref{macvar}) of $\Psi_\mu(x,p)$ and $\Psi_{{\scriptscriptstyle{1/2}}}(x,p)$ over the continuous index $p$.
\item[(B)]We tried to simplify the calculations of regularized propagators. We could do without the four-vector function $\Psi'_\mu(x,p)$ which we introduced solely to be able to use the same functions $t(p^2)$ and $f(p^2)$ in ${\cal L}_1$ and ${\cal L}_{{\scriptscriptstyle{1/2}}}$. We introduced $\ldp$ to make ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ itself real-valued, not only its action real as required.
\item[(C)]The Euler-Lagrange equations of ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ resemble the Boltzmann integro-differential transport equation, which can better model rapidly varying, ``ultra-high-energy'', macroscopic fluid phenomena than the differential equations of motion of fluid dynamics. (To this end it uses an infinite number of fields to take some  account of the underlying microscopic behaviour.) Euler-Lagrange equations of ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ may be regarded as classical transport equations of motion for the one-particle distribution of some infinitesimal entities, such as X-ons surmised to underly all physical phenomena by Feynman\cite{Feynm}. Which all are physical motivations for the type of Lagrangian we constructed; we discuss them in detail in Ref.~\cite{mi001}.
\end{itemize}

Using the Euler-Lagrange equations of ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ and proceeding as in Ref.~\onlinecite{mi002}, we calculate the dependence of $\Psi_\mu(x,p)$ and  $\Psi'_\mu(x,p)$ on $J_\mu(x)$, and of $\Psi_{{\scriptscriptstyle{1/2}}}(x,p)$ on $J_e(x)$. Thereby we can infer that the Feynman propagator for the four-vector field $A_\mu(x)$ defined by (\ref{macvar}) equals
\begin{equation}
   -i (2\pi)^{-4} \Four{g}_1 \, {\delta_{\mu\nu} + \Four{\mu}^{-2} k_\mu k_\nu\over k^2 + \Four{\mu}^2 } \,,
	\label{phpro}
\end{equation}
\begin{equation}
   \Four{g}_1(k^2) \equiv q_1 s_1^{-2} I_{10} I_{20}^{-2}\,, \qquad
   \Four{\mu}(k^2) \equiv |s_1|^{-1} I_{20}^{-1} \,,
\end{equation}
where $I_{mn}(k^2)$ is an analytic function of the complex variable $k^2$ such that
\begin{equation}
   I_{mn}(k^2) = 2 \pi^2 \Lambda^{-m} \int_0^\infty y^{m+n}
      f^2(y) t^{-m}(y) [ \sqrt{ 1 + \Lambda^{-2} k^2 y t^{-2}(y)}
      + 1]^{-m} dy
   \label{Imn}
\end{equation}
for $k^2 > 0$; and the Feynman propagator for the bispinor field $\psi(x)$ defined by (\ref{macvar}) equals
\begin{equation}
   -i (2\pi)^{-4} \Four{g}_{{\scriptscriptstyle{1/2}}} \, { - i\gamma^\mu k_\mu + \Four{m} \over
       k^2  + \Four{m}^2 } \,,
   \label{elpro}
\end{equation}
\begin{equation}
   \Four{g}_{{\scriptscriptstyle{1/2}}}(k^2) \equiv q_{{\scriptscriptstyle{1/2}}} s_{{\scriptscriptstyle{1/2}}}^{-1} I_{10}I_{20}^{-1}\,,
      \qquad \Four{m}(k^2) \equiv s_{{\scriptscriptstyle{1/2}}}^{-1} \{ 1 - s_{{\scriptscriptstyle{1/2}}}^2 [
      I_{10} I_{11}  + {\textstyle{1\over4}} k^2 I_{20}^2 ] \}
      I_{20}^{-1} \,;
\end{equation}
where $k^2$ has to be replaced everywhere with $k^2 - i\epsilon$, by the Feynman prescription.

If functions $t(p^2)$ and $f(p^2)$ are such that
\begin{equation}
   \int_0^\infty f^2(y) t(y) \, | \sqrt y /t(y)|^{l+1} dy = 0
   \label{ftpog}
\end{equation}
for $l=0, -1, \ldots,-n$, then for complex values of $k$ as $|k^2| \to \infty$:
\begin{equation}
   \left| \Four{g}_1 {\delta_{\mu\nu} + \Four{\mu}^{-2} k_\mu k_\nu
	\over k^2 + \Four{\mu}^2} \right| = O(|k^2|^{(1-n)/2}) \,,
   \qquad
   \left| \Four{g}_{{\scriptscriptstyle{1/2}}} \, {\Four{m} - i\gamma^\mu k_\mu
      \over k^2 + \Four{m}^2 } \right| = O(|k^2|^{-n/2}) \,.
   \label{phreg}
\end{equation}

When the function $y/t^2(y)$ takes only a finite number of real values $v_i$, $i = 1, 2, \ldots$, we can explicitly evalute integrals (\ref{Imn}); we obtain
\begin{equation}
   I_{mn}(k^2) = \Lambda^{-m} \sum_{i} A_{mni} v_i^{m} [ \sqrt{ 1 + \Lambda^{-2} v_i k^2 } + 1]^{-m} \,,
   \label{Imnexample}
\end{equation}
where $A_{mni}$ are real constants. Considering such a case, we can show that for any $\mu^2$, $m^2$ and integer $n$, there exist functions $f(p^2)$ and $t(p^2)$, and constants $s_1$, $s_{{\scriptscriptstyle{1/2}}}$, $q_1$, $q_{{\scriptscriptstyle{1/2}}}$, and $\Lambda_0 > 0$ such that the propagators (\ref{phpro}) and (\ref{elpro}) with $\Lambda > \Lambda_0$ are regularizations of spin 1 and spin $1\over 2$ propagators (\ref{PDeq}) such that: (i)~they have properties analogous to those of propagator (\ref{scpro}), and (ii)~there is a positive constant $k_0^2$ such that for all $k^2 \ge -\Lambda^2 k_0^2$ the functions $I_{mn}(k^2)$, $\Four{g}_{{\scriptscriptstyle{1/2}}}(k^2)$, $\Four{\mu}(k^2)$, $\Four{g}_1(k^2)$, and $\Four{m}(k^2)$ are real. In such a case: (i)~The constants $s_1$, $s_{{\scriptscriptstyle{1/2}}}$, $q_1$, and $q_{{\scriptscriptstyle{1/2}}}$ are such that
\begin{equation}
   \Four{\mu}^2(-\mu^2) = \mu^2 \,, \qquad
   \Four{m}^2(-m^2) = m^2 \,,
   \label{cond1}
\end{equation}
\begin{equation}
   \Four{g}_{{\scriptscriptstyle{1/2}}}(-\mu^2) = 1 + d\Four{\mu}^2(k^2 = -\mu^2)/ dk^2 \,,
   \qquad
   \Four{g}_1(-m^2) = 1 + d\Four{m}^2(k^2 = -m^2)/ dk^2 \,.
   \nonumber
\end{equation}
So the propagators (\ref{phpro}) and (\ref{elpro}) have poles at $k^2 = -\mu^2 $ and $k^2 = - m^2$, where their behaviour is given by the spin 1 and spin $1\over 2$ propagators (\ref{PDeq}) with $\epsilon = 0$. (ii)~The difference between spin 1 propagator and propagator (\ref{phpro}) depends on the value of $\Lambda$ so that it satisfies relations analogous to (\ref{regpr}); and the same goes for spin $1\over 2$ propagators. (iii)~The propagators (\ref{phpro}) and (\ref{elpro}) are analytic functions of $k^2$ that (a)~are not continuous everywhere across the negative real axis, (b)~have no additional singularities to those of spin 1 and spin $1\over 2$ propagators (\ref{PDeq}), and (c)~satisfy relations (\ref{phreg}). For any integer $n \ge 3$, their K\"all\'en-Lehman integral representations are superconvergent: in $x$-space we can decompose the Feynman propagators (\ref{phpro}) and (\ref{elpro}) into positive and negative energy parts without contact terms\cite{Hooft}.

\section{Physically plausible regularization of QED}

To obtain a perturbative S-matrix of quantum-electrodynamic phenomena based on the Lagrangian ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$, say $S_{{\scriptscriptstyle{\rm TR}}}$, we use the 't Hooft-Veltman definition of an S-matrix\cite{Hooft}. In view of results of Sec.III, there are functions $f(p^2)$ and $t(p^2)$, and constants $s_1$, $s_{{\scriptscriptstyle{1/2}}}$, $q_1$, $q_{{\scriptscriptstyle{1/2}}}$, and $\Lambda$ such that the n-point Green functions of ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ and the corresponding S-matrix $S_{{\scriptscriptstyle{\rm TR}}}$ have the following properties:
\begin{itemize}
\item[(i)]As the Lagrangian ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ has the same interaction and source terms as the QED Lagrangian ${\cal L}_{{\scriptscriptstyle{\rm QED}}}$, they are expressed in terms of QED diagrams with the spin 1 and spin $1\over 2$ propagators (\ref{PDeq}) replaced with their regularizations (\ref{phpro}) and (\ref{elpro}), whereas the vertices are the same as in QED, i.e., $(2\pi)^4 \gamma_\mu$; so all diagrams are finite.
\item[(ii)]As the propagators (\ref{phpro}) and (\ref{elpro}), and higher-order 2-point Green functions of ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ have no additional singularities, $S_{{\scriptscriptstyle{\rm TR}}}$ relates the same particles as the S-matrix of QED with massive photons in unitary gauge: electrons and positrons, each with two possible polarization vectors, and massive photons with three possible polarization vectors; none of them with wrong metric or statistics.
\item[(iii)]N-point Green functions are causal and $S_{{\scriptscriptstyle{\rm TR}}}$ is unitary to any order in the fine structure constant. To show this we may follow the t Hooft-Veltman proof for the HV-method\cite{Hooft}, since the propagators (\ref{phpro}) and (\ref{elpro}) admit the K\"all\'en-Lehman representation. \item[(iv)]$S_{{\scriptscriptstyle{\rm TR}}}$ is charge and total four-momentum conserving since its vertices are such.
\item[(v)]$S_{{\scriptscriptstyle{\rm TR}}}$ is Lorentz-invariant, since the propagators (\ref{phpro}) and (\ref{elpro}) commute with Lorentz transformations and the vertices are Lorentz-invariant.
\item[(vi)]In the asymptote $\Lambda \to \infty$, the propagators (\ref{phpro}) and (\ref{elpro}) behave the same way as required by Bogoliubov and Shirkov\cite{Bogol} of the Pauli-Villars--regularized spin 1 and spin $1\over 2$ propagators when their auxiliary masses tend to infinity in renormalization.
\end{itemize}
So, $S_{{\scriptscriptstyle{\rm TR}}}$ is a result of a pp-theory as defined in Section~I. This theory can be regarded as a physically plausible regularization of QED based on a physically motivated modification ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ of QED Lagrangian ${\cal L}_{{\scriptscriptstyle{\rm QED}}}$.

In view of (vi), we expect that we can compute by renormalization the renormalized n-point Green functions of QED with massless photons from the n-point Green functions of ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ by choosing an appropriate dependence of $e$, $s_1$, $s_{{\scriptscriptstyle{1/2}}}$, $q_1$, and $q_{{\scriptscriptstyle{1/2}}}$ on $\Lambda$, and then limiting $\Lambda \to \infty$ and the renormalized photon mass to zero. However, it is an open question whether the functions $f(p^2)$ and $t(p^2)$ must have also some additional properties for the photon third polarization vector to decouple in the limit of negligible photon mass\cite{Veltm}.

\section{Comments}

Generalizing the 't Hooft and Veltman method of unitary regulators we have shown, for the first time as far as we know, that one can regularize QED in accordance with the basic tenets of theoretical physics by suitably modifying the free part of QED Lagrangian. As we mentioned in Sec.III, the physical motivation for such modification has been the Feynman surmise about X-ons, and the Boltzmann improvement on fluid dynamics by the transport theory based on his equation.

Within the framework of quantum field theory as defined by 't Hooft and Veltman\cite{Hooft}, the Lagrangian ${\cal L}_{{\scriptscriptstyle{\rm TR}}}$ is related to the physical world solely through the perturbatively defined scattering matrix $S_{{\scriptscriptstyle{\rm TR}}}$. We see no physical properties of $S_{{\scriptscriptstyle{\rm TR}}}$ that require the spectral function (\ref{KLrho}) and the Hamiltonians corresponding to free Lagrangians ${\cal L}_1$ and ${\cal L}_{{\scriptscriptstyle{1/2}}}$ (which are not free-particle Lagrangians) to be positive as they turn out to be within the framework of canonical formalism\cite{Cao}.

The need for a regularization of QED that would result in a physically plausible model was felt very strongly by the founders of QED, Dirac and Heisenberg, already some sixty-five years ago\cite{Cao}. But neither they nor their contemporaries succeded in getting rid of the ultraviolet divergencies by a physicaly motivated modification of the QED Lagrangian. In the late 1940s, however, Tomonaga, Schwinger and Feynman ``solved'' the problem of QED ultraviolet divergencies through renormalization---a solution which does not require regularization to be physically plausible, and removes all parameters characteristic of regularization. As they obtained spectacularly succesful formulas for quantum-electrodynamic phenomena, the problem of finding a physically plausible, Lagrangian-based regularization of QED was not so urgent any more. As there had been no progress whatsoever towards a solution of this problem, it mainly came to be considered as practically unsolvable\cite{Cao}; those who hoped otherwise were often considered ``irrational'', as Isham, Salam, and Strathdee\cite{Salam} complained twenty-five years later. Thus nowadays, as far as we know, no quantum-field theorist, excepting the string theorist, pays much attention to this problem, which many of the preceding generations---e.g., Dirac, Heisenberg, Landau, Pauli, and Salam, to mention some---still hoped to be solved somehow someday\cite{Cao}. But the string theorists abandon one of the basic premises of conventional physics, the four-dimensionality of space-time. We have shown, however, that such drastic steps may be avoided when modifying QED Lagrangian to get rid of ultraviolet divergencies. But the question remains which modification of the type considered is the most appropriate for better describing quantum-electrodynamic phenomena at higher energies than the conventional QED, and what is its content.

\section{acknowledgement}

Authors greatly appreciate discussions with M. Polj\v sak and B. Bajc and their suggestions.

redpajama_set_name: RedPajamaArXiv


text:
Final Fantasy Pixel Remaster Series Coming to PS4, Switch
in Gaming News
The Final Fantasy Pixel Remaster Series, remastered versions of the first six Final Fantasy games and previously only available on PC via Steam and mobile, will be coming to PlayStation 4 and Nintendo Switch in the spring, publisher Square Enix said in a press release on Monday. Square Enix will also release physical versions in limited quantities via its online store, including a $260 Anniversary Edition.
Latest Humble Bundle Features 7 Survival Games For $15
The Dead Space Remake May Be the Best Video Game Remake Ever
The Pixel Remaster Series aims to keep the retro 8-bit visuals of the original six Final Fantasy titles — released between 1987 and 1994 on systems including the Nintendo Entertainment System, Super NES and the Sony PlayStation — while bringing some visual enhancements and quality-of-life improvements. These included updated graphics, a rearranged soundtrack overseen by composer Nobuo Uematsu, improved gameplay, modernized UI and auto-battle options.
Square Enix didn't immediately respond to a request for comment.
The retro aesthetic has been a popular trend in gaming for some time. It's especially popular with indie titles as generally 2D games are easier to make than full 3D ones. The "HD-2D" aesthetic has also gained in popularity, where a game will have blocky 2D visuals with some 3D effects baked into the design. Games using HD-2D include 2018's Octopath Traveler and 2022's Live A Live.
It's a style that blends hardware-constrained design of the '80s and '90s and pushes it to its modern max. It's proven to be a strong formula for Square Enix, with Octopath Traveler selling 3 million units and Live A Live selling 500,000 so far. Square Enix is working on Octopath Traveler 2, and fans are hoping the beloved '90s titles such as Chrono Trigger will also get the HD-2D treatment.
Both the standard physical edition and the Anniversary Edition are available for preorder on the Square Enix store. The standard edition, which runs for $75, will include all six games on either a PS4 disc or Switch cartridge. The $260 Anniversary Edition will include a physical version of the Remaster Series, a two-disc vinyl record set, an artbook, a pixel figure set and a lenticular sleeve, all packaged inside the anniversary box.
Humble Bundle has launched the Survival Instinct Game Bundle, which bands together a total of $170 value across seven games...
Whether you played the original Dead Space or not, you're gonna want to play the remake. For the uninitiated, the original...
Today's Wordle Answer (#586) – January 26, 2023
Who doesn't enjoy a little Thursday Wordle action every now and again? The answer on January 24 is not kind...
Xbox's Carbon Aware Update Is Great but Can We Take Its Climate Goals Seriously?
Over the past few years, the world's biggest video game companies and games studios have been taking more and more...


can be invaluable in debugging network problems.
Fix: Add a new fxp_stats struct and add in new amounts fxp_stats_update().
changes to the error counters.
>	can be invaluable in debugging network problems.
>	changes to the error counters.
>	Add a new fxp_stats struct and add in new amounts fxp_stats_update().
should be hidden behind a compile time option?
> >	can be invaluable in debugging network problems.
> >	changes to the error counters.
> >	Add a new fxp_stats struct and add in new amounts fxp_stats_update().
> should be hidden behind a compile time option?
>> should be hidden behind a compile time option?
>That would be fine with me.
MIB and made available via sysctl like what is done inside the if_ed driver.
> MIB and made available via sysctl like what is done inside the if_ed driver.
>  MIB and made available via sysctl like what is done inside the if_ed driver.
anyway for collision stats). Plus, this is only done once a second.
One question I had is do you know what the dot3Compliance field means?
Please take a look at let me know what you think.
With bugmeister hat on, reassign from inactive committer.
expose controller specific MAC counters.


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text:
Deméter se refiere a:
 En la mitología griega, Deméter era la diosa de la agricultura.
 En astronomía, (1108) Demeter es un asteroide del cinturón de asteroides.
 También en astronomía, Deméter fue un nombre alternativo de Lisitea, una de las lunas de Júpiter.


text:
using System;
using System.Collections;
using System.Text;
using System.Collections.Generic;
using System.Linq;
using Microsoft.VisualStudio.TestTools.UnitTesting;
using Rally.RestApi.Response;
using Rally.RestApi.Json;

namespace Rally.RestApi.Test
{
	/// <summary>
	/// Summary description for Example
	/// </summary>
	[TestClass]
	public class Example
	{
		public Example()
		{
			//
			// TODO: Add constructor logic here
			//
		}

		private TestContext testContextInstance;

		/// <summary>
		///Gets or sets the test context which provides
		///information about and functionality for the current test run.
		///</summary>
		public TestContext TestContext
		{
			get
			{
				return testContextInstance;
			}
			set
			{
				testContextInstance = value;
			}
		}

		#region Additional test attributes
		//
		// You can use the following additional attributes as you write your tests:
		//
		// Use ClassInitialize to run code before running the first test in the class
		// [ClassInitialize()]
		// public static void MyClassInitialize(TestContext testContext) { }
		//
		// Use ClassCleanup to run code after all tests in a class have run
		// [ClassCleanup()]
		// public static void MyClassCleanup() { }
		//
		// Use TestInitialize to run code before running each test
		// [TestInitialize()]
		// public void MyTestInitialize() { }
		//
		// Use TestCleanup to run code after each test has run
		// [TestCleanup()]
		// public void MyTestCleanup() { }
		//
		#endregion

		/// <summary>
		/// This sample method is also provided in the Sandcastle documentation. If you make
		/// changes here, please ensure they are propagated to there as well.
		/// </summary>
		[TestMethod]
		[Ignore]
		public void ExampleMethodText()
		{
			string username = "paul@acme.com";
			string password = "Just4Rally";
			// Initialize the REST API. You can specify a web service version if needed in the constructor.
			RallyRestApi restApi = new RallyRestApi();
			restApi.Authenticate(username, password, "https://preview.rallydev.com", proxy: null, allowSSO: false);

			//Create an item
			DynamicJsonObject toCreate = new DynamicJsonObject();
			toCreate["Name"] = "My Defect";
			CreateResult createResult = restApi.Create("defect", toCreate);

			//Update the item
			DynamicJsonObject toUpdate = new DynamicJsonObject();
			toUpdate["Description"] = "This is my defect.";
			OperationResult updateResult = restApi.Update(createResult.Reference,
											toUpdate);

			//Get the item
			DynamicJsonObject item = restApi.GetByReference(createResult.Reference);

			//Query for items
			Request request = new Request("defect");
			request.Fetch = new List<string>() { "Name", "Description", "FormattedID" };
			request.Query = new Query("Name", Query.Operator.Equals, "My Defect");
			QueryResult queryResult = restApi.Query(request);
			foreach (var result in queryResult.Results)
			{
				//Process item as needed
			}

			//Delete the item
			OperationResult deleteResult = restApi.Delete(createResult.Reference);
		}
	}
}

redpajama_set_name: RedPajamaGithub


text:
AP: Ten things to know for today
Your daily look at late-breaking news, upcoming events and the stories that will be talked about today: Updated Dec 14, 2015 at 8:19 AM
AP: Ten things to know today
'Trumbo' leads Screen Actor Guild nominations
The Hollywood blacklist drama "Trumbo" scored a leading three Screen Actors Guild Awards nominations on Wednesday, and sleeper contenders "Beasts of No Nation" and "Straight Outta Compton" entered the awards conversation in a real way when both were nominated for best ensemble drama. Updated Dec 9, 2015 at 10:34 AM
Time's Person of the Year is Angela Merkel
German Chancellor Angela Merkel has been named Time's Person of the Year, praised by the magazine for her leadership on everything from Syrian refugees to the Greek debt crisis. Updated Dec 9, 2015 at 8:08 AM
AP: 10 Things to Know for Today
Your daily look at late-breaking news, upcoming events and the stories that will be talked about today: Updated Dec 9, 2015 at 7:59 AM
AP: Remembering John Lennon w/ Video
The death of John Lennon still reverberates as a defining moment for a generation and for the music world. Updated Dec 8, 2015 at 8:54 AM
Kendrick the King: Rapper leads Grammys with 11 nominations (with full list of nominees)
Kendrick Lamar is the king of the Grammys: The rapper is the leading nominee for the 2016 awards with 11, including album of the year for "To Pimp a Butterfly" and song of the year for "Alright." Updated Dec 7, 2015 at 8:13 AM
AP Source: Woman in shooting pledged allegiance to IS
The woman who carried out the San Bernardino massacre with her husband had pledged allegiance to the Islamic State group and its leader on Facebook, a U.S. law enforcement official said Friday, providing the strongest evidence to date that the rampage may have been a terrorist attack. Updated Dec 4, 2015 at 2:05 PM
Manager: Ex-Stone Temple Pilots frontman Weiland dead at 48
Scott Weiland, the former frontman for the Stone Temple Pilots and Velvet Revolver, has died. He was 48. Updated Dec 4, 2015 at 8:58 AM
US adds healthy 211K jobs; unemployment steady at low 5 pct.
The U.S. economy generated another month of solid hiring in November, making it highly likely that the Federal Reserve will raise interest rates from record lows this month. Updated Dec 4, 2015 at 8:20 AM
Pious California killer showed no outward signs of violence
With a young wife, infant daughter and government job, Syed Farook appeared to have arrived at a sweet-spot in life. Friends knew the 28-year-old by his quick smile, his devotion to his Muslim religion and earnest talk about cars he would restore. Updated Dec 4, 2015 at 8:16 AM


As the Indian spa industry continues to grow at an astounding pace, it's now essential to constantly remain updated on all the news. Spa Mantra helps you stay current.
Every developing industry has its unique set of challenges, deficiencies, and accomplishments. Spa Mantra delves in-depth into the issues that plague the Indian spa industry. .
These individuals have carved a niche for themselves in this industry. Spa Mantra talks to the movers and shakers in the spa industry, getting them to spill their secrets for success..
New ingredients, new technologies, new equipments, new techniques and new sciences are always coming to the fore. Spa Mantra weeds outs the temporary fads from the sustainable trends. .


text:
About Flip Diving
Flip Diving is an internet flash web sports sport. The sport has lively 3D graphics and especially detailed character animations.
In this game, there are 10 characters however you can only pick the conventional character at the beginning. To unlock the rest of the personality, you'll have to play the game and complete assignments.
There are multiple stages in the game and every stage has its own unique terrain for you to go through. To clear a stage, you'll be required to jump while concurrently doing flips and landing on the appointed area. Be aware that if your back comes in contact with the water, you are going to lose.
There are coins on the screen that you can get by visiting the locations which have them. The coins may be used to spin a wheel and then unlock more spectacular-looking flips.
Note that after every point, the coins will be placed in harder to reach places, near challenges like cliffs, rocks on the surface of the water… and should you jump in these obstacles then it'll be game over.