text:
Professor Andreas Fring
Professor of Mathematical Physics
School of Science & Technology Department of Mathematics
a.fring@city.ac.uk
Professor Andreas Fring E217, Drysdale Building [E]
Professor Andreas Fring studied physics at the Technische Universität München and the University of London. He received a PhD in theoretical physics in 1992 from Imperial College London. He became a member of the Department of Mathematics in 2004, where he was promoted to Reader in 2005 and subsequently to Professor of Mathematical Physics in 2008.
Before joining City University London he held postdoc positions between 1992 and 1994 at the Universidade de São Paulo (São Carlos, Brazil) and the University of Wales (Swansea, UK). From 1994 until 2004 he was Wissenschaftlicher Mitarbeiter in the Department of Physics at the Freie Universität Berlin.
Latest Talks
• 22/06/2022, PT-symmetry in quantum and nonlinear systems
(Cinvestav, Mexico) [video]
• 04/11/2021, CPT-symmetry in quantum field theory
(London Theory Institute, UK) [video]
• 23/09/2021, Complex solitons in integrable systems with real energies
(International Centre for Theoretical Science, Bangalore, India) [video]
• 22/04/2021, Pseudo-Hermitian Hamiltonians in Quantum Physics
(virtual seminar on Pseudo-Hermitian Hamiltonians in Quantum Physics, UK) [video]
• 06/01/2021, N-extended Lorentzian Kac-Moody algebras and their associated Toda field theories
(Afulnahue, Chile) [video]
• 14/07/2015, A unifying E2-quasi-exactly solvable model
(Israel Institute for Advanced Studies, Jerusalem, Israel) [video]
• 06/11, Quantum Physics with non-Hermitian operators (Dresden, Germany)>
• 09/11, PT Quantum Mechanics Symposium (Heidelberg, Germany)
• 01/12, UK-Japan winter school (Oxford, UK)
PhD Theoretical Physics, Imperial College London, United Kingdom, 1992
MSc Theoretical Physics, Imperial College London, United Kingdom, 1989
BSc Physics, University of London, United Kingdom, 1988
Vordiplom Physics, Technical University of Munich, Germany, 1986
Professor, City, University of London, 2008 – present
Reader, City, University of London, 2005 – 2008
Lecturer, City, University of London, 2004 – 2005
C1 Research & Teaching Assistant, Free University of Berlin, 1994 – 2004
Senior Research Assistant, University of Wales, 1993 – 1994
Research Assistant, University of Sao Paulo, 1992 – 1993
Research Assistant, Imperial College London, 1992
Teaching at City University London
- Dynamical Systems [MA3608]
- Mathematical Methods [MA3605]
- Mathematics [AS1051]
- Integrable Systems [MAM611]
- Geometry & Vectors [MA1607] (05-09)
- Programming Excel/VBA [MA1603] (04-05)
- Advanced Certificate in Mathematics and Statistics (04-06)
His main field of research is mathematical physics with a focus on integrable quantum field theories and quantum mechanics. He co-authored around one hundred articles published in international journals and conference proceedings on topics including the form factor approach to integrable quantum field theories, factorised scattering theory, the thermodynamic Bethe Ansatz, representation theory of Virasoro algebras and Coxeter/Weyl reflection groups, high energy laser physics, pseudo-Hermitian quantum mechanical systems and noncommutative space-time structures.
- Integrable quantum field theory
- High intensity laser physics
- Pseudo-Hermitian Hamiltonian systems in quantum physics
Recent Keynote speeches and lectures
Pseudo-Hermitian Hamiltonians in Quantum Physics XII
July 2013, Koc University, Istanbul (Turkey)
International conference: Pseudo-Hermitian Hamiltonians in Quantum Physics XII pdf slides
Introduction to non-Hermitian Hamiltonian systems with PT symmetry, applications to integrable systems
January 2012, Oxford University (UK)
UK-Japan winter school : pdf slides
Takanobu Taira
Attendance: Jan 2019 – present, full-time
Thesis title: Non-Hermitian Quantum Field Theories
Role: 1st Supervisor
Rebecca Jade Tenney
Attendance: Oct 2018 – present, full-time
Thesis title: Non-classical and non-Hermitian aspects of electron-electron correlation in strong-field physics
Sam Whittington
Thesis title: Extensions of integrable quantum field theories based on Lorentzian Kac-Moody algebras
Julia Cen
Thesis title: Integrable systems with PT-symmetries
Thomas Frith
Thesis title: Unitary time-evolution in non-Hermitian quantum systems
Hamish Forbes
Attendance: Oct 2016 – present
Thesis title: The Bach equations in spin-coefficient form
Andrea Cavaglia
Attendance: Oct 2011 – Oct 2015, full-time
Thesis title: Nonsemilinear one-dimensional PDEs: analysis of PT deformed models and numerical study of compactons
Further information: This thesis is based on the work done during my PhD studies and is roughly divided in two independent parts. The first part consists of Chapters 1 and 2 and is based on the two papers Cavaglià et al. [2011] and Cavaglià & Fring [2012], concerning the complex PT-symmetric
deformations of the KdV equation and of the inviscid Burgers equation, respectively. The second part of the thesis, comprising Chapters 3 and 4, contains a review and original numerical studies on the properties of certain quasilinear dispersive PDEs in one dimension with compacton solutions.
The subjects treated in the two parts of this work are quite different, however a common theme, emphasised in the title of the thesis, is the occurrence of nonsemilinear PDEs. Such equations are characterised by the fact that the highest derivative enters the equation in
a nonlinear fashion, and arise in the modeling of strongly nonlinear natural phenomena such as the breaking of waves, the formation of shocks and crests or the creation of liquid drops. Typically, nonsemilinear equations are associated to the development of singularities and
non-analytic solutions. Many of the complex deformations considered in the first two chapters
are nonsemilinear as a result of the PT deformation. This is also a crucial feature of the compacton-supporting equations considered in the second part of this work.
This thesis is organized as follows. Chapter 1 contains an introduction to the field of PT-symmetric quantum and classical mechanics, motivating the study of PT-symmetric deformations of classical systems. Then, we review the contents of Cavaglià et al. [2011] where we explore travelling waves in two family of complex models obtained as PT-symmetric deformations of the KdV equation. We also illustrate with many examples the connection between the periodicity of orbits and their invariance under PTsymmetry.
Chapter 2 is based on the paper Cavaglià & Fring [2012] on the PTsymmetric deformation of the inviscid Burgers equation introduced in Bender & Feinberg [2008]. The main original contribution of this chapter is to characterise precisely how the deformation affects the
gradient catastrophe. We also point out some incorrect conclusions of the paper Bender & Feinberg [2008].
Chapter 3 contains a review on the properties of nonsemilinear dispersive PDEs in one space dimension, concentrating on the compacton solutions discovered in Rosenau & Hyman [1993]. After an introduction, we present some original numerical studies on the K(2, 2) and K(4, 4) equations. The emphasis is on illustrating the different type of phenomena exhibited by the solutions to these models. These numerical experiments confirm previous results on the properties of compacton-compacton collisions. Besides, we make some original observations,
showing the development of a singularity in an initially smooth solution.
In Chapter 4 , we consider an integrable compacton equation introduced by Rosenau in Rosenau [1996]. This equation has been previously studied numerically in an unpublished work by Hyman and Rosenau cited in Rosenau [2006]. We present an independent numerical study, confirming the claim of Rosenau [2006] that travelling compacton equations to this equation do not contribute to the initial value problem. Besides, we analyse the local conservation laws of this
equation and show that most of them are violated by any solution having a compact, dynamically evolving support. We confirm numerically that such solutions, which had not been described before, do indeed exist.
Finally, in Chapter 5 we present our conclusions and discuss open problems related to this work.
Sanjib Dey
Attendance: Oct 2011 – Sep 2014, full-time
Thesis title: Quantum mechanics and quantum field theory in noncommutative space
Further information: Intuitive arguments involving standard quantum mechanical uncertainty relations suggest that at length scales close to the Planck length, strong gravity effects limit the spatial as well as temporal resolution smaller than fundamental length scale, leading to space-space as well as spacetime uncertainties. Space-time cannot be probed with a resolution beyond this scale i.e. space-time becomes "fuzzy" below this scale, resulting into noncommutative spacetime. Hence it becomes important and interesting to study in detail the structure of such noncommutative spacetimes and their properties, because it not only helps us to improve our understanding of the Planck scale physics but also helps in bridging standard particle physics with physics at Planck scale.
Our main focus in this thesis is to explore different methods of constructing models in these kind of spaces in higher dimensions. In particular, we provide a systematic procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing non-commutative spaces. The representations for the corresponding operators obey algebras whose uncertainty relations lead to minimal length, areas and volumes in phase space, which are in principle natural candidates of many different approaches of quantum gravity. We study some explicit models on these types of non-commutative spaces, in particular, we provide solutions of three dimensional harmonic oscillator as well as its decomposed versions into lower dimensions. Because the solutions are computed in these cases by utilising the standard Rayleigh-Schrodinger perturbation theory, we investigate a method afterwards to construct models in an exact manner. We demonstrate three characteristically different solvable models on these spaces, the harmonic oscillator, the manifestly non-Hermitian Swanson model and an intrinsically non-commutative model with Poschl-Teller type potential. In many cases the operators are not Hermitian with regard to the standard inner products and that is the reason why we use PT -symmetry and pseudo-Hermiticity property, wherever applicable, to make them self-consistent well designed physical observables. We construct an exact form of the metric operator, which is rare in the literature, and provide Hermitian versions of the non-Hermitian Euclidean Lie algebraic type Hamiltonian systems. We also indicate the region of broken and unbroken PT -symmetry and provide a theoretical treatment of the gain loss behaviour of these types of systems in the unbroken PT -regime, which draws more attention to the experimental physicists in recent days.
Apart from building mathematical models, we focus on the physical implications of noncommutative theories too. We construct Klauder coherent states for the perturbative and nonperturbative noncommutative harmonic oscillator associated with uncertainty relations implying minimal lengths. In both cases, the uncertainty relations for the constructed states are shown to be saturated and thus imply to the squeezed coherent states. They are also shown to satisfy the Ehrenfest theorem dictating the classical like nature of the coherent wavepacket. The quality of those states are further underpinned by the fractional revival structure which compares the quality of the coherent states with that of the classical particle directly. More investigations into the comparison are carried out by a qualitative comparison between the dynamics of the classical particle and that of the coherent states based on numerical techniques. We find the qualitative behaviour to be governed by the Mandel parameter determining the regime in which the wavefunctions evolve as soliton like structures. We demonstrate these features explicitly for the harmonic oscillator, the Poschl-Teller potential and a Calogero type potential having singularity at the origin, we argue on the fact that the effects are less visible from the mathematical analysis and stress that the method is quite useful for the precession measurement required for the experimental purpose. In the context of complex classical mechanics we also find the claim that "the trajectories of classical particles in complex potential are always closed and periodic when its energy is real, and open when the energy is complex", which is demanded in the literature, is not in general true and we show that particles with complex energies can possess a closed and periodic orbit and particles with real energies can produce open trajectories.
Monique Smith
Thesis title: Antilinear deformations of Coxeter groups with application to Hamiltonian systems
Further information: The thesis provides several different systematic methods for constructing complex root spaces that remain invariant under an antilinear transformation. The first method is based on any element of the Weyl group, which is extended to factorizations of the Coxeter element and a reduced Coxeter element thereafter. An antilinear deformation method for the longest element of the Weyl group is provided. The last construction method leads to an alternative construction for q-deformed roots. Completed in 2012.
Paulo Eduardo Gonçalves de Assis
Thesis title: Non-Hermitian Hamiltonians in Field Theory
Further information: This thesis is centred around the role of non-Hermitian Hamiltonians in Physics both at the quantum and classical levels. In our investigations of two-level models we demonstrate [1] the phenomenon of fast transitions developed in the PT -symmetric quantum brachistochrone problem may in fact be attributed to the non-Hermiticity of evolution operator used, rather than to its invariance under PT operation. Transition probabilities are calculated for Hamiltonians which explicitly violate PT -symmetry. When it comes to Hilbert spaces of infinite dimension, starting with non-Hermitian Hamiltonians expressed as linear and quadratic combinations of the generators of the su(1; 1) Lie algebra, we construct [2] Hermitian partners in the same similarity class. Alongside, metrics with respect to which the original Hamiltonians are Hermitian are also constructed, allowing to assign meaning to a large class of non-Hermitian Hamiltonians possessing real spectra. The finding of exact results to establish the physical acceptability of other non-Hermitian models may be pursued by other means, especially if the system of interest cannot be expressed in terms of Lie algebraic elements. We also employ [3] a representation of the canonical commutation relations for position and momentum operators in terms of real-valued functions and a noncommutative product rule of differential form. Besides exact solutions, we also compute in a perturbative fashion metrics and isospectral partners for systems of physical interest. Classically, our efforts were concentrated on integrable models presenting PT - symmetry. Because the latter can also establish the reality of energies in classical systems described by Hamiltonian functions, we search for new families of nonlinear differential equations for which the presence of hidden symmetries allows one to assemble exact solutions. We use [4] the Painleve test to check whether deformations of integrable systems preserve integrability. Moreover we compare [5] integrable deformed models, which are thus likely to possess soliton solutions, to a broader class of systems presenting compacton solutions. Finally we study [6] the pole structure of certain real valued nonlinear integrable systems and establish that they behave as interacting particles whose motion can be extended to the complex plane in a PT -symmetric way.
Bender, C.M., Dorey, P.E., Dunning, C., Fring, A., Hook, D.W., Jones, H.F. … Tateo, R. (2019). PT Symmetry. WORLD SCIENTIFIC (EUROPE). ISBN 978-1-78634-595-0.
Dey, S., Fring, A. and Hussin, V. (2018). A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length. Springer Proceedings in Physics (pp. 209–242). Springer International Publishing. ISBN 978-3-319-76731-4.
Fring, A. and Frith, T. (2018). Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime. Journal of Physics A: Mathematical and Theoretical, 51(26), pp. 265301–265301. doi:10.1088/1751-8121/aac57b .
Cen, J., Correa, F. and Fring, A. (2017). Degenerate multi-solitons in the sine-Gordon equation. Journal of Physics A: Mathematical and Theoretical, 50(43), pp. 435201–435201. doi:10.1088/1751-8121/aa8b7e .
[publisher's website]
Fring, A. and Frith, T. (2017). Mending the broken PT-regime via an explicit time-dependent Dyson map. Physics Letters A, 381(29), pp. 2318–2323. doi:10.1016/j.physleta.2017.05.041 .
Fring, A., Cen, J. and Correa, F. (2017). Time-delay and reality conditions for complex solitons. Journal of Mathematical Physics, 58, pp. 32901–32901. doi:10.1063/1.4978864 .
Bagarello, F. and Fring, A. (2017). From pseudo-bosons to pseudo-Hermiticity via multiple generalized Bogoliubov transformations. International Journal of Modern Physics B, 31(12), pp. 1750085–1750085. doi:10.1142/S0217979217500850 .
Fring, A. and Frith, T. (2017). Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians. Physical Review A, 95(1). doi:10.1103/physreva.95.010102 .
Dey, S., Fring, A. and Hussin, V. (2017). Nonclassicality versus entanglement in a noncommutative space. International Journal of Modern Physics B, 31(01), pp. 1650248–1650248. doi:10.1142/s0217979216502489 .
Cen, J. and Fring, A. (2016). Complex solitons with real energies. Journal of Physics A: Mathematical and Theoretical, 49(36), pp. 365202–365202. doi:10.1088/1751-8113/49/36/365202 .
Correa, F. and Fring, A. (2016). Regularized degenerate multi-solitons. Journal of High Energy Physics, 2016(9). doi:10.1007/jhep09(2016)008 .
Fring, A. and Moussa, M.H.Y. (2016). Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians. Physical Review A, 93(4). doi:10.1103/physreva.93.042114 .
Fring, A. (2016). A Unifying E2-Quasi Exactly Solvable Model. pp. 235–248. doi:10.1007/978-3-319-31356-6_15 .
Dey, S., Fring, A. and Gouba, L. (2015). Milne quantization for non-Hermitian systems. Journal of Physics A: Mathematical and Theoretical, 48(40), pp. 40–40. doi:10.1088/1751-8113/48/40/40ft01 .
Fring, A. (2015). E2-quasi-exact solvability for non-Hermitian models. Journal of Physics A: Mathematical and Theoretical, 48(14), pp. 145301–145301. doi:10.1088/1751-8113/48/14/145301 .
Dey, S. and Fring, A. (2014). Noncommutative quantum mechanics in a time-dependent background. Physical Review D, 90(8). doi:10.1103/physrevd.90.084005 .
Dey, S., Fring, A. and Mathanaranjan, T. (2014). Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra. Annals of Physics, 346, pp. 28–41. doi:10.1016/j.aop.2014.04.002 .
Bender, C.M., Fring, A. and Komijani, J. (2014). Nonlinear eigenvalue problems. Journal of Physics A: Mathematical and Theoretical, 47(23), pp. 235204–235204. doi:10.1088/1751-8113/47/23/235204 .
Fring, A. and Bagarello, F. (2013). A non self-adjoint model on a two dimensional
noncommutative space with unbound metric. Physical Review A: Atomic, Molecular and Optical Physics, 88, p. 42119. doi:10.1103/PhysRevA.88.042119 .
Fring, A. and Dey, S. (2013). Bohmian quantum trajectories from coherent states. Physical Review A: Atomic, Molecular and Optical Physics, 88, p. 22116. doi:10.1103/PhysRevA.88.022116 .
Fring, A., Dey, S, and Khantoul, B. (2013). Hermitian versus non-Hermitian representations for minimal length uncertainty relations. Journal of Physics A: Mathematical and Theoretical, 46, pp. 335304–335304. doi:10.1088/1751-8113/46/33/335304 .
Fring, A., Dey, S., Gouba, L. and Castro, P.G. (2013). Time-dependent q-deformed coherent states for generalized uncertainty relations. Physical Review D: Particles, Fields, Gravitation and Cosmology, 87. doi:10.1103/PhysRevD.87.084033 .
Fring, A. (2013). PT-symmetric deformations of integrable models. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371, p. 20120046. doi:10.1098/rsta.2012.0046 .
Fring, A. and Smith, M. (2012). Non-Hermitian multi-particle systems from complex root spaces. Journal of Physics A: Mathematical and Theoretical, 45(8). doi:10.1088/1751-8113/45/8/085203 .
Dey, S. and Fring, A. (2012). Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations. Physical Review D - Particles, Fields, Gravitation and Cosmology, 86(6). doi:10.1103/PhysRevD.86.064038 .
Cavaglia, A. and Fring, A. (2012). PT-symmetrically deformed shock waves. Journal of Physics A: Mathematical and Theoretical, 45(44). doi:10.1088/1751-8113/45/44/444010 .
Bender, C., Fring, A., Günther, U. and Jones, H. (2012). Quantum physics with non-Hermitian operators. Journal of Physics A: Mathematical and Theoretical, 45(44). doi:10.1088/1751-8113/45/44/440301 .
Cavaglia, A., Fring, A. and Bagchi, B. (2011). PT-symmetry breaking in complex nonlinear wave equations and their deformations. J PHYS A-MATH THEOR, 44(32). doi:10.1088/1751-8113/44/32/325201 .
Fring, A., Gouba, L. and Scholtz, F.G. (2010). Strings from position-dependent noncommutativity. J PHYS A-MATH THEOR, 43(34). doi:10.1088/1751-8113/43/34/345401 .
Fring, A. and Smith, M. (2010). Antilinear deformations of Coxeter groups, an application to Calogero models. J PHYS A-MATH THEOR, 43(32). doi:10.1088/1751-8113/43/32/325201 .
Castro-Alvaredo, O.A. and Fring, A. (2009). A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field. J PHYS A-MATH THEOR, 42(46). doi:10.1088/1751-8113/42/46/465211 .
Assis, P.E.G. and Fring, A. (2009). Non-Hermitian Hamiltonians of Lie algebraic type. J PHYS A-MATH THEOR, 42(1). doi:10.1088/1751-8113/42/1/015203 .
Conference papers and proceedings (7)
Castro Alvaredo, O. and Fring, A. (2003). Integrable models with unstable particles. July, Faro (Portugal).
Castro Alvaredo, O. and Fring, A. (2002). Applications of quantum integrable systems. September, Moscow (Russia).
Castro Alvaredo, O. and Fring, A. (2002). Conductance from Non-perturbative Methods II. July, São Paulo (Brazil).
Castro Alvaredo, O. and Fring, A. (2002). Aspects of locality in the form factor program. World Scientific, Singapore.
Castro Alvaredo, O. and Fring, A. (2001). Mutually local fields from form factors. December, Edinburgh, UK.
Castro Alvaredo, O. and Fring, A. (2001). Mutually local fields from form factors. October, Tianjin, China.
Castro Alvaredo, O. and Fring, A. (2001). Mutually local fields from form factors. September, Yerevan (Armenia).
Fring, A. and Tenney, R. (2022). Lewis–Riesenfeld invariants for PT-symmetrically coupled oscillators from two-dimensional point transformations and Lie algebraic expansions. Journal of Mathematical Physics, 63(12). doi:10.1063/5.0110312 .
Fring, A., Taira, T. and Tenney, R. (2022). Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories. Physics Letters A, 452. doi:10.1016/j.physleta.2022.128458 .
Correa, F., Fring, A. and Taira, T. (2022). Moduli spaces for PT-regularized solitons. Journal of High Energy Physics, 2022(10). doi:10.1007/jhep10(2022)109 .
Correa, F., Fring, A. and Taira, T. (2022). Linearly stable and unstable complex soliton solutions with real energies in the Bullough-Dodd model. Nuclear Physics B, 979, pp. 115783–115783. doi:10.1016/j.nuclphysb.2022.115783 .
Fring, A. and Taira, T. (2022). Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory. The European Physical Journal Plus, 137(6). doi:10.1140/epjp/s13360-022-02889-z .
Cen, J., Correa, F., Fring, A. and Taira, T. (2022). Stability in integrable nonlocal nonlinear equations. Physics Letters A, 435. doi:10.1016/j.physleta.2022.128060 .
Fring, A. and Tenney, R. (2021). Infinite series of time-dependent Dyson maps. Journal of Physics A: Mathematical and Theoretical, 54(48), pp. 485201–485201. doi:10.1088/1751-8121/ac31a0 .
Correa, F., Fring, A. and Taira, T. (2021). Complex BPS Skyrmions with real energy. Nuclear Physics B, 971, pp. 115516–115516. doi:10.1016/j.nuclphysb.2021.115516 .
Fring, A. and Taira, T. (2021). Non-Hermitian gauge field theories and BPS limits. Journal of Physics: Conference Series, 2038(1), pp. 12010–12010. doi:10.1088/1742-6596/2038/1/012010 .
Fring, A. and Tenney, R. (2021). Exactly solvable time-dependent non-Hermitian quantum systems from point transformations. Physics Letters A, 410, pp. 127548–127548. doi:10.1016/j.physleta.2021.127548 .
Fring, A. and Whittington, S. (2021). Lorentzian Toda field theories. Reviews in Mathematical Physics, 33(6). doi:10.1142/s0129055x21500173 .
Fring, A. and Tenney, R. (2021). Perturbative approach for strong and weakly coupled time-dependent for non-Hermitian quantum systems. Physica Scripta, 96(4), pp. 45211–45211. doi:10.1088/1402-4896/abe259 .
Fring, A. and Taira, T. (2020). Complex BPS solitons with real energies from duality. Journal of Physics A: Mathematical and Theoretical, 53, pp. 455701–455701. doi:10.1088/1751-8121/abb92a .
Fring, A. and Taira, T. (2020). 't Hooft-Polyakov monopoles in non-Hermitian quantum field theory. Physics Letters B, 807, pp. 135583–135583. doi:10.1016/j.physletb.2020.135583 .
Fring, A. and Whittington, S. (2020). n-Extended Lorentzian Kac–Moody algebras. Letters in Mathematical Physics, 110(7), pp. 1689–1710. doi:10.1007/s11005-020-01272-2 .
Fring, A. and Tenney, R. (2020). Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators. Physics Letters A, 384(21), pp. 126530–126530. doi:10.1016/j.physleta.2020.126530 .
Cen, J., Correa, F. and Fring, A. (2020). Nonlocal gauge equivalence: Hirota versus extended continuous Heisenberg and Landau–Lifschitz equation. Journal of Physics A: Mathematical and Theoretical, 53(19), pp. 195201–195201. doi:10.1088/1751-8121/ab81d9 .
Fring, A. and Frith, T. (2020). Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator. Modern Physics Letters A, 35(08), pp. 2050041–2050041. doi:10.1142/s0217732320500418 .
Fring, A. and Taira, T. (2020). Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories. Physical Review D, 101(4). doi:10.1103/physrevd.101.045014 .
Fring, A. and Tenney, R. (2020). Time-independent approximations for time-dependent optical potentials. The European Physical Journal Plus, 135(2). doi:10.1140/epjp/s13360-020-00143-y .
Cen, J. and Fring, A. (2020). Multicomplex solitons. Journal of Nonlinear Mathematical Physics, 27(1), pp. 17–35. doi:10.1080/14029251.2020.1683963 .
Fring, A. and Taira, T. (2020). Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories. Nuclear Physics B, 950, pp. 1–1. doi:10.1016/j.nuclphysb.2019.114834 .
Cen, J. and Fring, A. (2019). Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation. Physica D: Nonlinear Phenomena, 397, pp. 17–24. doi:10.1016/j.physd.2019.05.005 .
Cen, J., Correa, F. and Fring, A. (2019). Integrable nonlocal Hirota equations. Journal of Mathematical Physics, 60(8), pp. 81508–81508. doi:10.1063/1.5013154 .
Fring, A. and Frith, T. (2019). Eternal life of entropy in non-Hermitian quantum systems. Physical Review A, 100(1). doi:10.1103/physreva.100.010102 .
Cen, J., Fring, A. and Frith, T. (2019). Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems. Journal of Physics A: Mathematical and Theoretical, 52(11), pp. 115302–115302. doi:10.1088/1751-8121/ab0335 .
Bagchi, B. and Fring, A. (2019). Quantum, noncommutative and MOND corrections to the entropic law of gravitation. International Journal of Modern Physics B, 33(05), pp. 1950018–1950018. doi:10.1142/s0217979219500188 .
Fring, A. and Frith, T. (2018). Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians. Physics Letters A. doi:10.1016/j.physleta.2018.10.043 .
Fring, A. and Frith, T. (2018). Metric versus observable operator representation, higher spin models. The European Physical Journal Plus, 133(2). doi:10.1140/epjp/i2018-11892-4 .
(2018). Coherent States and Their Applications. . doi:10.1007/978-3-319-76732-1 .
Fring, A. and Moussa, M.H.Y. (2016). Non-Hermitian Swanson model with a time-dependent metric. Physical Review A, 94(4). doi:10.1103/physreva.94.042128 .
Khantoul, B. and Fring, A. (2015). Time-dependent massless Dirac fermions in graphene. Physics Letters A, 379(42), pp. 2704–2706. doi:10.1016/j.physleta.2015.08.011 .
Bagarello, F. and Fring, A. (2015). Generalized Bogoliubov transformations versus D-pseudo-bosons. Journal of Mathematical Physics, 56(10), pp. 103508–103508. doi:10.1063/1.4933242 .
Fring, A. (2015). A new non-Hermitian E2-quasi-exactly solvable model. Physics Letters A, 379(10-11), pp. 873–876. doi:10.1016/j.physleta.2015.01.008 .
Dey, S., Fring, A. and Mathanaranjan, T. (2014). Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type. International Journal of Theoretical Physics, 54(11), pp. 4027–4033. doi:10.1007/s10773-014-2447-4 .
Fring, A. and Dey, S. (2013). The Two-dimensional Harmonic Oscillator on a Noncommutative Space with Minimal Uncertainties. Acta Polytechnica: journal of advanced engineering, 53, pp. 268–276.
Dey, S., Fring, A. and Gouba, L. (2012). PT-symmetric non-commutative spaces with minimal volume uncertainty relations. Journal of Physics A: Mathematical and Theoretical, 45(38). doi:10.1088/1751-8113/45/38/385302 .
Fring, A. and Smith, M. (2011). PT Invariant Complex E (8) Root Spaces. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 50(4), pp. 974–981. doi:10.1007/s10773-010-0542-8 .
Fring, A., Gouba, L. and Bagchi, B. (2010). Minimal areas from q-deformed oscillator algebras. J. Phys. A: Math. Theor.43:425202, 2010. doi:10.1088/1751-8113/43/42/425202 .
Assis, P.E.G. and Fring, A. (2010). Compactons versus solitons. Pramana - Journal of Physics, 74(6), pp. 857–865. doi:10.1007/s12043-010-0078-8 .
Bagchi, B. and Fring, A. (2009). Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems. PHYS LETT A, 373(47), pp. 4307–4310. doi:10.1016/j.physleta.2009.09.054 .
Assis, P.E.G. and Fring, A. (2009). From real fields to complex Calogero particles. J PHYS A-MATH THEOR, 42(42). doi:10.1088/1751-8113/42/42/425206 .
Fring, A. (2009). Particles versus fields in PT-symmetrically deformed integrable systems. PRAMANA-JOURNAL OF PHYSICS, 73(2), pp. 363–373. doi:10.1007/s12043-009-0128-2 .
Assis, P.E.G. and Fring, A. (2009). Integrable models from PT -symmetric deformations. J PHYS A-MATH THEOR, 42(10). doi:10.1088/1751-8113/42/10/105206 .
Bagchi, B. and Fring, A. (2009). Comment on "Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty". SYMMETRY INTEGR GEOM, 5. doi:10.3842/SIGMA.2009.089 .
Bagchi, B. and Fring, A. (2008). PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation. J PHYS A-MATH THEOR, 41(39). doi:10.1088/1751-8113/41/39/392004 .
Assis, P.E.G. and Fring, A. (2008). Metrics and isospectral partners for the most generic cubic PT -symmetric non-Hermitian Hamiltonian. Journal of Physics A: Mathematical and Theoretical, 41(24). doi:10.1088/1751-8113/41/24/244001 .
Assis, P.E.G. and Fring, A. (2008). The quantum brachistochrone problem for non-Hermitian Hamiltonians. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 41(24). doi:10.1088/1751-8113/41/24/244002 .
Fring, A., Jones, H. and Znojil, M. (2008). 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics: Preface. Journal of Physics A: Mathematical and Theoretical, 41(24). doi:10.1088/1751-8121/41/24/240301 .
Fring, A. and Znojil, M. (2008). PT -symmetric deformations of Calogero models. Journal of Physics A: Mathematical and Theoretical, 41(19). doi:10.1088/1751-8113/41/19/194010 .
Castro Alvaredo, O., Fring, A. and Göhmann, F. (2008). On the absence of simultaneous reflection and transmission in integrable impurity systems. Submited to Phys. Lett..
Fring, A. (2007). PT-symmetry and Integrability. Acta Polytechnica 47 (2007) 44-49.
Faria, C.F.M. and Fring, A. (2007). Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: From the time-independent to the time-dependent quantum mechanical formulation. LASER PHYS, 17(4), pp. 424–437. doi:10.1134/S1054660X07040196 .
Fring, A. (2007). PT -symmetric deformations of the Korteweg-de Vries equation. Journal of Physics A: Mathematical and Theoretical, 40(15), pp. 4215–4224.
Fring, A. and Manojlovic, N. (2006). G(2)-Calogero-Moser Lax operators from reduction. J NONLINEAR MATH PHY, 13(4), pp. 467–478. doi:10.2991/jnmp.2006.13.4.1 .
Fring, A. (2006). A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models. Modern Physics Letters A, 21(8), pp. 691–699. doi:10.1142/S0217732306019682 .
Fring, A. and Korff, C. (2006). Non-crystallographic reduction of generalized Calogero-Moser models. J PHYS A-MATH GEN, 39(5), pp. 1115–1131. doi:10.1088/0305-4470/39/5/007 .
Figueira De Morisson Faria, C. and Fring, A. (2006). Time evolution of non-Hermitian Hamiltonian systems. Journal of Physics A: Mathematical and General, 39(29), pp. 9269–9289. doi:10.1088/0305-4470/39/29/018 .
De Morisson Faria, C.F. and Fring, A. (2006). Isospectral hamiltonians from moyal products. Czechoslovak Journal of Physics, 56(9), pp. 899–908. doi:10.1007/s10582-006-0386-x .
Fring, A. and Korff, C. (2005). Affine Toda field theories related to Coxeter groups of noncrystallographic type. NUCL PHYS B, 729(3), pp. 361–386. doi:10.1016/j.nuclphysb.2005.08.044 .
Castro-Alvaredo, O. and Fring, A. (2005). Chaos in the thermodynamic Bethe ansatz. PHYS LETT A, 334(2-3), pp. 173–179. doi:10.1016/j.physleta.2004.11.009 .
Fring, A. (2005). Supersymmetric integrable scattering theories with unstable particles. J HIGH ENERGY PHYS, (1). doi:10.1088/1126-6708/2005/01/030 .
Castro Alvaredo, O. and Fring, A. (2005). Integrable models with unstable particles. Progress in Mathematics, 237, p. 59.
Fring, A. and Korff, C. (2004). Exactly solvable potentials of Calogero type for q-deformed Coxeter groups. J PHYS A-MATH GEN, 37(45), pp. 10931–10949. doi:10.1088/0305-4470/37/45/012 .
Castro-Alvaredo, A. and Fring, A. (2004). On vacuum energies and renomalizability in integrable quantum field theories. NUCL PHYS B, 687(3), pp. 303–322. doi:10.1016/j.nuclphysb.2004.04.005 .
Castro-Alvaredo, O.A. and Fring, A. (2004). Applications of quantum integrable systems. International Journal of Modern Physics A, 19(SUPPL. 2), pp. 92–116. doi:10.1142/S0217751X04020336 .
Castro-Alvaredo, O.A., Dreißig, J. and Fring, A. (2004). Integrable scattering theories with unstable particles. European Physical Journal C, 35(3), pp. 393–411.
Castro Alvaredo, O. and Fring, A. (2004). Universal boundary reflection amplitudes. Nucl. Phys., B682, p. 551. doi:10.1016/j.nuclphysb.2004.01.009 .
Castro-Alvaredo, O.A. and Fring, A. (2003). Breathers in the elliptic sine-Gordon model. Journal of Physics A: Mathematical and General, 36(40), pp. 10233–10249. doi:10.1088/0305-4470/36/40/008 .
Castro-Alvaredo, O.A. and Fring, A. (2003). Rational sequences for the conductance in quantum wires from affine Toda field theories. Journal of Physics A: Mathematical and General, 36(26). doi:10.1088/0305-4470/36/26/101 .
Castro-Alvaredo, O.A., Figueira de Morisson Faria, C. and Fring, A. (2003). Relativistic treatment of harmonics from impurity systems in quantum wires. Physical Review B - Condensed Matter and Materials Physics, 67(12). doi:10.1103/PhysRevB.67.125405 .
Castro-Alvaredo, O. and Fring, A. (2003). From integrability to conductance, impurity systems. Nuclear Physics B, 649(3), pp. 449–490. doi:10.1016/S0550-3213(02)01029-5 .
Castro Alvaredo, O. and Fring, A. (2003). Conductance from Non-perturbative Methods II. JHEP ,PRHEP-unesp2002/015; cond-mat/0210592.
Castro Alvaredo, O. and Fring, A. (2003). Conductance from Non-perturbative Methods I. JHEP ,PRHEP-unesp2002/010; cond-mat/0210599.
Fring, A. (2002). Mutually local fields from form factors. International Journal of Modern Physics B, 16(14-15), pp. 1915–1924. doi:10.1142/S0217979202011639 .
Castro Alvaredo, O. and Fring, A. (2002). Finite temperature correlation functions from form factors. Nucl. Phys., B636, p. 611.
Castro Alvaredo, O. and Fring, A. (2002). Unstable particles versus resonances in impurity systems, conductance in quantum wires. Journal of Physics: Condensed Matter, 14. doi:10.1088/0953-8984/14/47/101 .
Castro Alvaredo, O. and Fring, A. (2002). Scaling functions from q-deformed Virasoro characters. J. Phys., A35, p. 609. doi:10.1088/0305-4470/35/3/310 .
Fring, A. (2001). Thermodynamic Bethe ansatz and form factors for the homogeneous
sine-Gordon models. Nato Science Series, 35, pp. 139–153. doi:10.1007/978-94-010-0670-5_9 .
Castro-Alvaredo, O.A. and Fring, A. (2001). Form factors from free fermionic Fock fields, the Federbush model. Nuclear Physics B, 618(3), pp. 437–464.
Castro Alvaredo, O. and Fring, A. (2001). Constructing infinite particle spectra. Phys. Rev., D64. doi:10.1103/PhysRevD.64.085005 .
Castro Alvaredo, O. and Fring, A. (2001). Decoupling the SU(N)2-homogeneous sine-Gordon model. Phys. Rev., D64. doi:10.1103/PhysRevD.64.085007 .
Castro Alvaredo, O. and Fring, A. (2001). Renormalization group flow with unstable particles. Phys. Rev., D63.
Castro Alvaredo, O. and Fring, A. (2001). Identifying the operator content, the Homogeneous sine-Gordon models. Nucl. Phys., B604, p. 367.
Fring, A. and Korff, C. (2000). Colour valued scattering matrices. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 477(1-3), pp. 380–386. doi:10.1016/S0370-2693(00)00226-4 .
Fring, A. and Korff, C. (2000). Large and small density approximations to the thermodynamic Bethe ansatz. Nuclear Physics B, 579(3), pp. 617–631. doi:10.1016/S0550-3213(00)00250-9 .
Bytsko, A.G. and Fring, A. (2000). Factorized combinations of Virasoro characters. Communications in Mathematical Physics, 209(1), pp. 179–205.
Fring, A., Korff, C. and Schulz, B.J. (2000). On the universal representation of the scattering matrix of affine toda field theory. Nuclear Physics B, 567(3), pp. 409–453.
Figueira De Morisson Faria, C., Fring, A. and Schrader, R. (2000). Existence criteria for stabilization from the scaling behaviour of ionization probabilities. Journal of Physics B: Atomic, Molecular and Optical Physics, 33(8), pp. 1675–1685.
Castro Alvaredo, O., Fring, A. and Korff, C. (2000). Form factors of the homogeneous sine-Gordon models. Phys. Lett., B484, p. 167.
Castro Alvaredo, O., Fring, A., Korff, C. and Miramontes, J.L. (2000). Thermodynamic Bethe ansatz of the homogeneous sine-Gordon models. Nucl. Phys., B575, p. 535.
Faria, C.F.D.M., Fring, A. and Schrader, R. (1999). Stabilization not for certain and the usefulness of bounds. Proc. 8-th Int. Conf. on Multiphothon Processes, ed. L.F. DiMauro et.al. (1999) 150.
Babujian, H., Fring, A., Karowski, M. and Zapletal, A. (1999). Exact form factors in integrable quantum field theories: The sine-Gordon model. Nuclear Physics B, 538(3), pp. 535–586. doi:10.1016/S0550-3213(98)00737-8 .
Fring, A., Korff, C. and Schulz, B.J. (1999). The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory. Nuclear Physics B, 549(3), pp. 579–612.
Figueira De Morisson Faria, C., Fring, A. and Schrader, R. (1999). Analytical treatment of stabilization. Laser Physics, 9(1), pp. 379–387.
Bytsko, A.G. and Fring, A. (1999). ADE spectra in conformal field theory. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 454(1-2), pp. 59–69.
Bytsko, A.G. and Fring, A. (1998). A Note on ADE-Spectra in Conformal Field Theory. Phys.Lett. B454 (1999) 59-69. doi:10.1016/S0370-2693(99)00300-7 .
Bytsko, A.G. and Fring, A. (1998). Thermodynamic Bethe Ansatz with Haldane Statistics. Nucl.Phys. B532 (1998) 588-608. doi:10.1016/S0550-3213(98)00531-8 .
Bytsko, A.G. and Fring, A. (1998). Anyonic interpretation of Virasoro characters and the thermodynamic Bethe ansatz. Nuclear Physics B, 521(3), pp. 573–591. doi:10.1016/S0550-3213(98)00222-3 .
Figueira De Morisson Faria, C., Fring, A. and Schrader, R. (1998). On the influence of pulse shapes on ionization probability. Journal of Physics B: Atomic, Molecular and Optical Physics, 31(3), pp. 449–464.
Belavin, A.A. and Fring, A. (1997). On the fermionic quasi-particle interpretation in minimal models of conformal field theory. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 409(1-4), pp. 199–205. doi:10.1016/S0370-2693(97)00879-4 .
Fring, A., Kostrykin, V. and Schrader, R. (1997). Ionization probabilities through ultra-intense fields in the extreme limit. Journal of Physics A: Mathematical and General, 30(24), pp. 8599–8610.
Fring, A. (1996). Braid relations in affine Toda field theory. International Journal of Modern Physics A, 11(7), pp. 1337–1352.
Fring, A., Kostrykin, V. and Schrader, R. (1996). On the absence of bound-state stabilization through short ultra-intense fields. Journal of Physics B: Atomic, Molecular and Optical Physics, 29(23), pp. 5651–5671.
Fring, A. and Koberle, R. (1994). Boundary Bound States in Affine Toda Field Theory. Int.J.Mod.Phys. A10 (1995) 739-752.
Fring, A. and Köberle, R. (1994). Factorized scattering in the presence of reflecting boundaries. Nuclear Physics B, 421(1), pp. 159–172.
Fring, A. and Köberle, R. (1994). Affine Toda field theory in the presence of reflecting boundaries. Nuclear Physics B, 419(3), pp. 647–662.
Fring, A., Johnson, P.R., Kneipp, M.A.C. and Olive, D.I. (1994). Vertex operators and soliton time delays in affine Toda field theory. Nuclear Physics B, 430(3), pp. 597–614.
Fring, A. (1993). Form Factors in Affine Toda Field Theories. .
Fring, A., Mussardo, G. and Simonetti, P. (1993). Form factors for integrable lagrangian field theories, the sinh-Gordon model. Nuclear Physics, Section B, 393(1-2), pp. 413–441. doi:10.1016/0550-3213(93)90252-K .
Fring, A., Mussardo, G. and Simonetti, P. (1993). Form factors of the elementary field in the Bullough-Dodd model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 307(1-2), pp. 83–90.
Fring, A. (1992). Couplings in Affine Toda Field Theories. .
Fring, A. and Olive, D.I. (1992). The fusing rule and the scattering matrix of affine Toda theory. Nuclear Physics B, 379(1-2), pp. 429–447.
Fring, A., Liao, H.C. and Olive, D.I. (1991). The mass spectrum and coupling in affine Toda theories. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 266(1-2), pp. 82–86.
Editorial activity (2)
Advisory board of Journal of Physics A.
Editorial board ISRN Mathematical Physics.
Keynote lectures/speeches (30)
PT-symmetry in quantum and nonlinear systems. Cinvestav, Mexico City, Mexico (2022). [video]
PT-symmetry in quantum and nonlinear systems. Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas del IPN, Mexico City, Mexico (2022). Graduate lecture
PT-symmetry in nonlinear systems. Bielefeld University, Germany (2022). Physikalisches Kolloquium
PT-symmetry in nonlinear systems. virtually at Wolfram (2022). Wolfram Physics Project colloquium
What do mathematical physicists do? An example: A generalised version of Heisenberg's uncertainty relation. Ark Academy, Wembley, London, UK (2022). Talk at local school
PT-symmetry in nonlinear systems. virtually at Bharathidasan University, India (2022). Lecture series in Nonlinear Dynamics
CPT-symmetry in quantum field theory. (virtual) London Theory Institute, UK (2021). Lecture Series, [video]
PT-symmetric quantum mechanics an introduction to time-dependent systems. virtually at Tecnológico de Monterrey, Mexico (2021). Quantum Fest 2021 International Conference on Quantum Phenomena, Quantum Control and Quantum Optics
[arXiv]
Complex solitons in integrable systems with real energies. (virtual) International Centre for Theoretical Science, Bangalore, India (2021). [video]
Degenerate and nonlocal soliton solutions from PT-symmetry. virtually University of Kent, UK (2021). SIG IX (Solitons @ work workshop)
Non-Hermitian gauge field theories and BPS limits. virtually University of Kent, UK (2021). Solitons at Work seminar
Non-Hermitian gauge field theories and BPS limits. (virtual) London, UK (2021). virtual seminar series on Pseudo-Hermitian Hamiltonians in Quantum Physics [video]
N-extended Lorentzian Kac-Moody algebras and their associated Toda field theories. (virtually) Afulnahue, Chile (2021). La Parte y el Todo [video]
Complex solitons in integrable systems with real energies, nonlocal gauge equivalence and BPS solutions from duality. vitually Singapore (2020). 11th DYNAMICS DAY Asia-Pacic
Goldstone's theorem and the Higgs mechanism in non-Abelian non-Hermitian quantum field theories. virtually University of York, UK (2020). Mathematics colloquium
Eternal life of entropy in time-dependent non-Hermitian quantum systems. Department of Theoretical Physics of the Nuclear Physics Institute, Rez, Czech Republic (2020). Doppler Institute Micro seminars
Goldstone's theorem and the Higgs mechanism in non-Abelian non-Hermitian quantum field theories. Czech Technical University, Prague, Czech Republic (2020). Mathematical Engineering seminar: Method of Algebra and Functional analysis in Applications
Nonlocal gauge equivalent integrable systems. Cardiff University, UK (2019). Mathematics Colloquium
Nonlocal gauge equivalent integrable systems. Centro de Ciencias de Benasque, Spain (2019). 7th International Workshop on new challenges in Quantum Mechanics: Integrability and Supersymmetry
Introduction to PT-quantum mechanics, deformations of integrable models. Universität Stuttgart, Germany (2019). Physikalisches Kolloquium
Introduction to PT-quantum mechanics, deformations of integrable models. Afunalhue, Chile (2019). La Parte y el Todo workshop
Time-dependent non-Hermitian systems, a status update. Bogoliubov Laboratory of Theoretical Physics of the JINR Dubna, Russia (2018). Supersymmetry in Integrable Systems - SIS'18
Time-dependent non-Hermitian systems a status update. International Centre for Theoretical Sciences, Bangalore, India (2018). Non-Hermitian Hamiltonians in Physics (PHHQP18) [video]
Introduction to PT-quantum mechanics, deformations of integrable models. Banaras Hindu University, Varanassi, India (2018). Physics colloquium
Minimal lengths, areas and volumes in noncommutative quasi-Hermitian systems. CIRM, Marseille, France (2016). Coherent States and their Applications: A Contemporary Panorama
PT-symmetry and integrability as reality conditions for complex solitons. Yukawa Institute for Theoretical Physics, Kyoto University, Japan (2016). Progress in Quantum Physics with Non-Hermitian Operators
A unifying E2-quasi-exactly solvable model. Yerevan State University, Armenia (2015). Supersymmetry in Integrable Systems - SIS'15 Slides
A unifying E2-quasi-exactly solvable model. Hebrew University of Jerusalem, Institute for Advanced Studies, Jerusalem, Israel (2015). Quantum (and Classical) Physics with Non-Hermitian Operators [video]
Noncommutative quantum mechanics in a time-dependent background. University of Ferhat Abbas, Setif, Algeria (2014). 14th International Workshop on Pseudo-Hermitian Hamiltonians
Non-Hermitian representations for noncommutative spaces. Koc University, Istanbul (Turkey) (2013). International conference: Pseudo-Hermitian Hamiltonians in Quantum Physics XII
Media appearances (3)
Video for Faculti Media TV. Hermitian versus Non-Hermitian representations for minimal length uncertainty relations
Faculti Media video
Interview in The Guardian. Must all post doc research have impact?
Article in the Guardian
City Review 2011. City review 2011, academic excellence


Battling with daily info-load issues myself, I have never been much of a fan of the whole Twitter thing. The idea is fine - an extension of the status line update informal communications channel that's been a part of online life since the first time that mainframes and minicomputers allowed their users to see what everyone else was doing.
Battling with daily info-load issues myself, I have never been much of a fan of the whole Twitter thing. The idea is fine - an extension of the status line update informal communications channel that's been a part of online life since the first time that mainframes and minicomputers allowed their users to see what everyone else was doing. But the practical effects of voluntarily immersing oneself in yet another layer of asynchronous noise (can you have synchronous noise?) did not appeal.
Nonetheless, about a month ago I finally allowed myself to be talked into Twittering. At least, I tried: the site was down.
I tried again, and managed to register. Since then, I've spent more time trying to make bits of it work than I have enjoying the service - and when it does work, it seems to have two modes: silence, and avalanche.
My latest experience has been just as daunting. The woman who talked me into trying it IM'd me asking "Can you get Googletalk working with it?".
No. I followed the online instructions: no good. I searched for enlightenment online, and found plenty of "Do this, and it will just work" recipes. Only it didn't.
Finally, I asked a friend. "IM's been down for weeks," he said. "First thing that goes when they have capacity issues. And they always have capacity issues." He then pointed me at the status.twitter.com page, which indeed listed IM as being offline. Of course, once he'd done that I immediately spotted the link to the status page on the main Twitter input. D'oh.
I have some sympathy for Twitter. Just not that much. Have a big success online, and you're riding the tiger: revenue doesn't scale with popularity, but by gosh your tech costs do. It's also not unknown for all sorts of architectural problems to appear once something gets properly wellied, and for them to take time and money to fix. Often, you'll have features that don't stand up and have to be turned off - or even abandoned. That's part of the game these days, and anyone who tries new services should be aware they're part of the Great Experiment, where nobody knows what's going to happen next.
So, Twitter, turn the darn things off. Remove the "Here's how to sign up to IM" options. Slap "Closed for renovations" over the thing. Don't leave your site as a guessing game. Don't expect people to find your status page - no, not even if you leave the link in plain sight. Consumer electronics manufacturers know that even if the first thing the punter sees when opening the box is a huge piece of paper with "READ ME FIRST!" written on it in 72 point letters of fire, that paper is effectively invisible. That's not what the punters are there for.
It is about managing expectations, and that's all about understanding how people work. Twitter doesn't - and for a service all about people's intimate behaviour, that's a killer flaw.


For many of us on this website the answer to this question might seem obvious: because they are awesome! It can't be denied that heels make you appear longer and leaner – and they give your silhouette great curves. But our modern love for sky-high stilettos might be more than just aesthetic.
One theory is that heels, which originated on the feet of the wealthy classes, are an indication that you do not have to work – or walk, for that matter. Some people even call them "limo shoes" due to the fact that those wearing high heels aren't likely to use common means of transportation. Accordingly, our attraction to high heels is due to our need to appear high class.
Are these reasons accurate? Tell us what you think! Why do you like high heels?
Should Wonder Woman Wear High Heels?


text:
Beginner's Guide to the Great Story (Part 10)
October 31, 2020 Tom Vander Well	Leave a comment
This week's Wayfarer Weekend podcast is the final episode of a ten-part series: Beginner's Guide to the Great Story. We wrap up the series with a brief introduction to the ever-intriguing subject of the book of Revelation and the topic of what the Bible has to say about the end times.
(WW) Beginner's Guide to the Great Story Part 10 – Wayfarer
BeginnerBibleEpistlesExplanationGreat StoryNew TestamentNewbiePodcastStudyTom Vander WellWayfarer
Lament (and Parenting)
October 30, 2020 Tom Vander Well	1 Comment
Lament (and Parenting) [CaD Ps 55] – Wayfarer
If an enemy were insulting me,
I could endure it;
if a foe were rising against me,
I could hide.
But it is you, a man like myself,
my companion, my close friend,
with whom I once enjoyed sweet fellowship
at the house of God…
Psalm 55:12-14 (NIV)
Thus far, in my entire life journey, I discovered that the process of releasing my adult children on to their own respective paths of life to be one of the most surprisingly difficult things I've ever experienced. It's not just about the loss of control and the fact that my child may choose paths unfitting my dreams, desires, and expectations. It's also the experience of catching glimpses of my own weaknesses and shortcomings as a parent, and the useless wonderings of "What if I had only…."
The greatest challenge of David's life was not the Bathsheba scandal which I talked about in the podcast on Psalm 51. Bathsheba gets top billing and is better known because it has all of the classic plot elements we love in a steamy Harlequin Romance. The greatest challenge of David's life is lesser known, but I personally find it even more fascinating because it is more intimate and complex. Late in David's life, he faces a coup de tête finds himself fleeing for his life, and almost loses his throne and his life to his very own son.
The story is found in 2 Samuel 13-19. Let me give you the Reader's Digest condensed version. The seeds of the rebellion are in David's own shortcomings as a father. Marriage and family looked very different for a monarch in ancient times. Not only was polygamy regularly practiced, but a monarch had the added layer of nations wanting to marry off daughters to other kings to establish diplomatic ties. David had eight wives, and at least 10 concubines. Which meant the palaces were teaming with princes and princesses who were half-brothers and half-sisters. Long story short, Prince Amnon had the hots for his sister, Princess Tamar. He rapes her, and then in his shame, he shuns Tamar and wants nothing to do with. He treated her like a prostitute. King David is furious according to the record, but he does nothing. He passively seems to ignore the whole thing.
Princess Tamar's older brother is Prince Absalom, and Absalom bottles up his rage against his half-brother Amnon, who raped his sister, and against his father who did nothing to justly deal with Amnon. The seeds of Prince Absalom's rage take root and grow into a plot to kill his brother and steal his father's kingdom. He succeeds at the former, and nearly succeeds with the latter.
In the process of his scheming to steal his father's throne, the Great Story records that Absalom spent a lot of time establishing allies among the rich, noble, and powerful people in the kingdom. Quietly, slowly he used his position and influence to create both debts and alliances so that when he pulled the trigger on his coup David had virtually no one supporting him.
We can't be certain, but the lyrics of David's song that we know as Psalm 55 seem as though they could very well have been penned during the time of Absalom's rebellion. David expresses that Jerusalem is a boiling cauldron of deceit, treachery, and violence. He feels the sting of an unnamed "companion" who he thought was a friend and ally, but turns out to have sold him out. It is certainly reasonable to think that he's referring to someone that Absalom convinced to aid in his rebellion.
Like many of David's songs, Psalm 55 is a personal lament. He is pouring out all of his emotions from despair, hurt, anguish, fear, confusion, and the desire to fly away from all of his troubles. In the pouring out of his deepest emotions he also is reminded of how faithful God had always been and the song ends with a simple proclamation of his unwavering trust.
One of the fascinating threads in the story of Absalom's rebellion is David's unwavering love for Absalom. Despite the fratricide, the rebellion, and the attempt to destroy David and take everything that was his, David ordered his men to be gentle with Absalom. When he heard Absalom had been killed, David wept and mourned to the point that his own General called David out for humiliating all of the soldiers who had been loyal to him.
In the quiet this morning I find myself contemplating the complex relationship between parents and children, especially as children mature into their own selves and lives. The whole story of David and his children Amnon, Tamar, and Absalom is a hot mess. There is so much of the story that is not told. Nevertheless, it reminds me of the intense and infinite love a parent feels for a child no matter the differences, conflicts, or chasms that emerge in the relationship.
Once again, there is no concrete evidence to directly correlate Psalm 55 with the story of Absalom's rebellion, nor is there concrete evidence to the contrary. Some mornings, I find that this is the way the chapter-a-day journey goes. The text connects me to one idea which leads down another path of thought, and I end up in an unintended destination of thought and Spirit. C'est lav ie.
Parenting is one of the grand adventures of this life journey. It has produced the greatest of joys and the deepest of sorrows. It has humbled me to my core, and has equipped Lady Sophia with some of the most powerful practicums for teaching me wisdom.
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Prayer of Desperation
October 29, 2020 Tom Vander Well	2 Comments
Prayer of Desperation (CaD Ps 54) – Wayfarer
Surely God is my help;
the Lord is the one who sustains me.
It could be argued that in King David's young adult years he was a loose archetype of the legendary character we know as Robin Hood. He is living in the wilderness with a rag-tag band of some 600 vagabonds, mercenaries, and outcasts. David's got a price on his head and mad-king Saul is hell-bent on killing his young rival whom he knows is God's anointed replacement to his throne.
The thing about having a big price on your head is that you never know who you can trust. David and his merry band of exiles have been on the move, trying to stay one step ahead of Saul and his army. While hiding in a region known as the Desert of Ziph, the people of that area see a prime opportunity to cash-in on the sizable bounty Saul has laid out for David's capture and strengthen their diplomatic ties with the current ruler.
In short order, David and his men find themselves on the run. Saul and his army are closing in. It's a dire situation and things look hopeless. In the midst of his desperation, David writes a song. It's the song we know as Psalm 54.
I love about Psalm 54 is short, sweet, and to the point. It's like a guttural prayer that surfaces in the heat of the moment. It's just seven short verses that begin with a plea for God's vindication and end with David's proclamation of faith that God will rescue David from his tight spot. As I've mentioned in previous posts, Hebrew songs like this were structured to be symmetrical with the center verse being the key to the entire thing. The center verse is the heart of what the songwriter is trying to express:
Along this life journey, I also encounter moments when I feel pinned down by circumstances stacked against me. There are times when I feel like I'm stumbling around with the darkness closing in. I have flashes when my prayer feels like Princess Leia's hologram.
In the quiet this morning I found myself ear-marking Psalm 54 for those times when I, like David, have the enemy bearing down on me and there are others who seem to be against me. David's song makes a great prayer of faith and assurance in the midst of desperation.
Psalm 54 is also a reminder that God does answer prayer. Just as Saul and his army were about to capture David and his men, a messenger arrives to tell Saul that a foreign army was raiding the land. Saul and his army had to stop their pursuit. David and his men escaped to a hideout in another area. It turns out that David's musical prayer was prophetic:
You have delivered me from all my troubles,
and my eyes have looked in triumph on my foes.
May you be blessed to find yourself delivered from your troubles today, my friend!
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Same Song, Only Different
Same Song, Only Different (CaD Ps 53) – Wayfarer
God scattered the bones of those who attacked you;
you put them to shame, for God despised them.
Psalm 53:5b (NIV)
Wendy and I really enjoy being fans. For us, the fun is in being loyal to our teams, following them, knowing the players, following the drama, cheering for them, and experiencing what ABC's Wide World of Sports used to describe each week as "the thrill of victory and the agony of defeat."
A few years ago we found ourselves feeling the emptiness in the depth of our Iowa winter. January through March always feels like a slog, but we realized that it was made worse for us because our Vikings' season was over and it would be April before our Cubs' would begin their annual campaign. For whatever reason, the NBA has never tripped our trigger. So, we decided it was time to join our son-in-law Clayton and give the English Premier League a shot.
We knew that for us the fun is in following a team, so we began researching the various teams in a search for the team to whom we would pledge our loyalty. It's surprising how many resources there are on the internet for Americans trying to choose a Premier League team. In the end, we chose to become fans of Liverpool FC (Football Club). And, as silly as it sounds, the clincher for us was the song.
One of the endearing things about Premier League is the singing. During most pre-covid matches when the stands are packed you'll hear the crowd singing. Not just a specific moment in the match, like singing Take Me Out to the Ballgame in the middle of the 7th Inning. Premier League fans often sing themselves hoarse through the entire match. There are typically different songs fans have for different players, and teams typically adopt a theme song.
Liverpool's theme song is Gerry and the Pacemaker's You'll Never Walk Alone which also happens to be a song from the Broadway Musical Carousel. Wendy and I discovered this fact in our research and then pulled up a YouTube video of the Liverpool crowd singing it before a match. We got goosebumps, and it sealed the deal. Two Liverpool fans were born.
So, you might be wondering to yourself, "Where on earth are you going with this?" Well, if you've followed my blog and/or podcast for anything length of time you know that I'm fond of saying that God's language is metaphor, and metaphor is layered with meaning. The song You'll Never Walk Alone is a great example.
For many people like Wendy and me, the song has been forever tied to the musical Carousel. A teenager growing up in the early 1960s might never have known it was from a Broadway musical, but the version by Gerry and the Pacemakers might have tremendous emotional ties to a crush they had on a boy or girl, dancing cheek-to-cheek at a school dance, or listening with friends on a crackly AM car radio as you scooped the loop. Then Liverpool takes the same song and it becomes an anthem of solidarity, loyalty, and community for fans of their football club around the world.
For me, the most interesting thing about today's chapter, Psalm 53, is that it is virtually identical to Psalm 14. If you put them side-by-side you'll notice that it's the same song, but verse 5 is different. Scholars believe that the nation took David's original and co-opted it after a national victory over armies who had sought to destroy them as in the story found in 2 Chronicles 20 when they were unexpectedly attacked by the army of Edom. When David wrote the song to mean one thing during his life and his generation, but a subsequent generation took the same song, the same lyrics, and made it about another thing.
In the quiet this morning, it has me thinking about something I've frequently observed in my perpetual journey through the Great Story. Something that had little or no meaning for me thirty years ago might suddenly be powerfully important for me today at this waypoint on Life's road. Things that meant one thing to me then might take on a whole new layer of meaning for me now. I'm so grateful to my mentors who taught me at the beginning of my spiritual journey that reading and studying the Great Story was not a one-and-done deal. "On it you shall meditate both day and night," says Joshua 1:8, the very first verse I memorized when I was 15. And, that's what I've tried to do, and it's made an unfathomable difference in both my spiritual journey and my life journey.
The Great Story meets me where I am every morning. A verse, or chapter, or passage can help me frame my past, make sense of my present, and direct my course for the future all at the same time.
Thanks for walking with me this morning and reminding me that "I'll never walk alone."
Go Liverpool! 🙂
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The Impotence to Respond
But God will break you down forever;
he will snatch and tear you from your tent;
he will uproot you from the land of the living.
Psalm 52:5 (NRSVCE)
David was hiding in a cave in the middle of a desolate wilderness with a rag-tag group of outcasts and mercenary warriors. He may have been God's anointed king, but the throne was still tightly under the control of his father-in-law, Saul, and Saul had made David public enemy number one. That left David scratching out a meager existence in the middle-of-nowhere as he hid from the powerful mad-king who wanted David dead.
In an act of desperation, David sneaks in to visit God's priest, Ahimelech. Like an enemy soldier seeking sanctuary in the protection of a church, David went to the place where the traveling tent sanctuary from the days of Moses was set up and serving as the center of worship. David sought God's divine guidance through the priest. David begged for help and was provided food as well as the sword of Goliath that was still housed there like a trophy.
It just so happened that a servant of Saul name Doeg was there and witnessed David's visit. Doeg goes to King Saul and tells him of David's visit and the assistance Ahimelech provided David. Saul confronts Ahimelech who attempts to argue that, as the king's son-in-law, the priest felt an obligation to assist David as an act of faithfulness to Saul. Saul rewards Ahimelech by telling Doeg to kill him, and all of God's priests living in the town, along with all of their wives and children. Saul has Doeg massacre an entire village of his own people and his own priests because one priest showed kindness to David.
One of Ahimelech's son's survives and seeks David in his hide-away cave He tells David of Doeg's visit to Saul and subsequent massacre. David, realizing that his visit to Ahimelech started the chain of events leading to the massacre, feels the weight of responsibility for his actions.
David, as he always did with his intense emotions, channels his feelings into a song which is known to us as Psalm 52. It's today's chapter.
David's song is fascinating in its structure. The first verse is David addressing Doeg and calling out his wickedness, arrogance, treachery, and deceit. The third and final verse is the contrast, with David claiming his standing in the right, trusting in God, and proclaiming that trust directly. In between the two verses is the central theme in which David hands Doeg over to God for God's judgment. He relinquishes vengeance and retribution to God.
In the quiet this morning, I couldn't help but put myself in David's shoes. David was in a position of impotence. He's hiding in a cave in the wilderness. He has no status. He has no standing. At this moment there is nothing that he can do in his own power to right the wrong that resulted from his actions. His only option is to cry out his emotions and ask God to right the wrong he is powerless to address himself.
What a powerful word picture. In this life journey I have found myself impotent to address and correct wrongs. Thankfully, the wrongs are trivial in comparison to the massacre of innocents David was dealing with. Nevertheless, I find in David an example to follow. Pouring out and expressing my rage, frustration, accusation and consciously handing over that which I am powerless to do to God.
As I contemplate David's story, and his lyrics, this morning I find myself with two connected thoughts into the day ahead:
First, Paul writing to the followers of Jesus in Rome, who were impotent agains a Roman Empire that would throw them to the lions in the Roman Circus and watch them being devoured for entertainment:
Don't hit back; discover beauty in everyone. If you've got it in you, get along with everybody. Don't insist on getting even; that's not for you to do. "I'll do the judging," says God. "I'll take care of it."
Romans 12:17-29 (MSG)
Second, the simple prayer of serenity:
God,
Grant me the serenity to accept the things I cannot change,
the courage to change the things I can,
and the wisdom to know the difference.
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A Psalm 51 Moment
The sacrifice acceptable to God is a broken spirit;
Psalm 51:17 (NRSVCE)
For anyone who does not know the story behind David's song, known to us as Psalm 51, it is critical in order to have a complete understanding of the lyrics.
First of all, David had been the "good guy" his entire life journey. As a boy God declared him "a man after my own heart" and God chose David, through the prophet Samuel, to be God's anointed king. David killed Goliath. David refused to raise his hand against King Saul and wait for God to fulfill the promise to give him the throne. David did everything right. David was devout. David was faithful. David was sincere. David was God's man through-and-through.
Until he wasn't.
The Reader's Digest version is this: From the roof of his palace he creeped out on a beautiful young woman taking a bath on a nearby rooftop. David used his power to find out who she was. She was the wife of one of David's soldiers, but the army was out on a military campaign and David knew it. David used his influence as King to invite her over. They had a one night stand. She ended up pregnant, and now a "no harm no foul" fling became a potentially Monica Lewinsky level political scandal.
The first step in the cover-up was to create the illusion of normal. David uses his commander-and-chief authority to give the woman's husband, a soldier named Uriah, a special leave to come home and take a break from the action. It turns out, however, that Uriah was a "good guy" and a "man of integrity" like David had always been. Perhaps David had been his role model. Uriah, thinking of all his buddies on the front-line who didn't get to come home and sleep with their wives, refuses to even go into his house.
Ironically, Uriah's integrity leads to David's further descent into depravity. To avoid his moral failure from coming to light and the scandal it would create, David sends Uriah back to the front with a sealed message to his general in the field. The message orders his general to place Uriah into the thick of the battle, order his fellow soldiers to abandon him, and ensure Uriah has an "honorable" death.
Uriah is buried with military honors. David makes a big deal out of caring for the widow of one of his soldiers by agreeing to marry and take care of her. Scandal averted and David is given the opportunity to improve his polling numbers and maintain his "good guy" image. David gets away it. No one is the wiser.
Except God.
God sends a prophet named Nathan to visit the King who regales David with the story of a wealthy land baron and sheep farmer who stole the only lamb of the poor tenant farmer next-door. David, angered, assures Nathan that the evil land baron will be forced to pay the victim back with four lambs for the one that was stolen.
Then Nathan informs David that the whole story was a metaphor and that he is the land baron in the story. He had a palace full of wives and thought he could steal poor Uriah's wife and cover the whole thing up. David is devastated and has to own up to what he has done. He pours out his guilt and plea for forgiveness into a song.
If you've never read Psalm 51 in the context of this story, I encourage you to take the minute or two required to read the lyrics of the song in their entirety right now while the story is fresh in your head.
One of the interesting things about this chapter-a-day journey is the experience of coming upon chapters that I know really well, and have read countless times in the past 40 years. Do they have any fresh layers of meaning for me at this particular waypoint of life's journey?
As I read this morning I kept hearkening back to one of David's psalms from a couple of weeks ago. I went back to Psalm 26 in the quiet this morning and read it again:
Vindicate me, O Lord,
for I have walked in my integrity,
and I have trusted in the Lord without wavering.
Prove me, O Lord, and try me;
test my heart and mind.
For your steadfast love is before my eyes,
and I walk in faithfulness to you.
Wow. What a contrast.
I know Psalm 51 really well. It's tatted on my left bicep as a reminder. I have a chapter of my own story that is a rough parallel of David's. I was the "good guy" who everyone knew was a Jesus freak, a moral puritan, and who walked the straight-and-narrow. I'm sure I was even guilty of waxing self-righteously in my own way like David did in Psalm 26. Then I found myself in a place I swore I'd never be found. I had my own Psalm 51 moment.
Along this spiritual journey, I've come to understand that I never really understood and experienced grace, forgiveness, and mercy until I hit rock-bottom and the veneer of self-righteousness was peeled away like the striking of a stage set. Like David, it came much further along in my journey, but I can now look back realize how important, make that essential, my own mistakes were in teaching me humility, empathy, mercy, and grace.
I enter another work week this morning soberly reminded of my own need of grace, as well as my need to extend it to others having their own Psalm 51 moments.
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The Religion Game
"Those who bring thanksgiving as their sacrifice honor me;
to those who go the right way
I will show the salvation of God."
As a child, my family regularly attended church where worship was held with lots of traditional, liturgical pomp. I even got to participate as I sang in the children's choir wearing my robe. Looking back with understanding, I have an appreciation for the metaphor and intent of all the liturgical devices, even the way the sanctuary was designed and laid out.
I went through the motions like everyone else. Sing this. Proceed to there. Sit down. Stand up. Say this. Sing this. Sit down. Read this. Stand up. Sing this. Sit down. Listen. Stand up. Sing this. Proceed there. Done. It happened every week with very little variation other than the words that were said or sang.
It was regular. It was rote. It was religious.
The problem was, I never thought much about it at all. It was what we did. I checked off the box along with every body else.
As I have ceaselessly journeyed through the Great Story, I'm always struck by the rather exhaustive system of sacrifices, offerings, rituals, and feasts that God dictates to the Hebrews through Moses. As I've studied them, I've come to appreciate the reason behind them and how they fit together in a cycle that led the Hebrews through specific thoughts and lessons about their relationship with God.
Nevertheless, there is sprinkled through the words of the psalmists and prophets a recurring theme that the people are doing all the things, but they're hearts aren't in it. They are making the sacrifices, offering the prescribed things at the prescribed times, going through the rituals, and attending the feasts. It was regular. It was rote. It was religious. The problem was that they weren't really thinking much about it.
Today's psalm was written to be sung as part of worship in the temple, but the songwriter, Asaph, is calling God's people out for their mindless, spirit-less dedication to going through the religious motions. The "thanksgiving" offerings are void of any real gratitude. The real sacrifice, the songwriter says, is a heart full of gratitude to God which motivates all the other rituals.
This was the same thing Jesus found in the religious leaders of His day. They were continually critical of Him for breaking the religious regulation they added to the ancient rules. Jesus repeatedly quoted God through the prophet Hosea to them: "Go and learn what this means," Jesus said, "'I desire mercy, not sacrifice.'"
Jesus was getting at the same thing as Asaph in today's psalm. Mindlessly going through religious motions is of no real value, and I believe that this is one of the reasons why denominations are imploding and churches are closing in record numbers. Just minutes ago our daughter sent the family a photo she took of an old church she and Clayton visited in a remote area of Scotland this past week. It's being turned into a brewery. The altar will be the bar. Some of my ancestors would have found that scandalous. I don't at all. As I have repeatedly written, Jesus made it clear that it was never supposed to be about bricks-and-mortar, but flesh-and-blood. It was never about the ritual, but the relationship. An honest, transparent, love-motivated conversation over a pint might be the most spiritual, Christ-honoring thing to happen in that building in a long time.
Jesus completely changed the game.
We keep changing it back.
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Wisdom & Winnowing
Wisdom and Winnowing (CaD Ps 49) – Wayfarer
When we look at the wise, they die;
fool and dolt perish together
and leave their wealth to others.
Over the past few years, I have watched, and assisted, as my parents' lives have gotten significantly smaller in footprint. From a giant ranch home where grandchildren hung out together and spent a week each summer at "grandma camp," to a townhouse, a two-bedroom apartment, and now a smaller apartment. With every subsequent move, there is a winnowing of life's material possessions.
"Does anyone want this?"
"What should we do with that?"
"Somebody might use that. Let's give it to the Many Hands Thrift Store."
"Seriously. Nobody wants that. Throw it in the dumpster."
Some time ago I was listening to a teacher who encouraged listeners to perform a virtual winnowing of life in your head. Think about everything you own. Not just the big items like homes, cars, and furniture, but the boxes of stuff in storage rooms, attics, and garages. Think about the collective contents of junk drawers, closet shelves, and storage bins. Having taken an exhaustive mental inventory, now consider where it's all going to end up, and who is going to own it, when you die. Note: Someone else will own everything that doesn't get pitched into the dumpster. And believe me, for many of us there will be a dumpster.
Today's chapter continues a string of ancient Hebrew song lyrics written for a specific purpose. Psalm 49 is one of just two songs in the anthology of 150 songs written as "Wisdom Literature." Across antiquity, sages throughout the Near East created proverbs, songs, parables, and literary works intended to teach and pass along wisdom.
As I shared in this chapter-a-day journey through the book of Proverbs (a classic example of "Wisdom Literature"), even in the Great Story wisdom is personified in a woman often referred to as Sophia. Wisdom Literature is typically marked by a calling out to or from wisdom as the songwriter does today in verses 3-4:
My mouth shall speak wisdom;
the meditation of my heart shall be understanding.
I will incline my ear to a proverb;
I will solve my riddle to the music of the harp.
The songwriter then challenges us as listeners and readers to consider the fact that rich-and-poor, wise-and-foolish, good-and-bad all end up in the same place and leave everything behind. Even the Egyptians who packed King Tut's tomb with stuff for him to use in the afterlife only ended up lining the pockets of Lord Carnarvon and the displays of various museums.
Of course, Lady Wisdom calls out to me to think about this in relationship to what it means for me today, and I hear the echo of Jesus in my soul:
"Don't hoard treasure down here where it gets eaten by moths and corroded by rust or—worse!—stolen by burglars. Stockpile treasure in heaven, where it's safe from moth and rust and burglars. It's obvious, isn't it? The place where your treasure is, is the place you will most want to be, and end up being.
Matthew 19-21 (MSG)
In the quiet this morning, I hear Wisdom, Jesus, and Holy Spirit whispering to my soul. The exercise of virtual winnowing needs to lead me to actual physical winnowing, or else they have simply wasted their collective breath.
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Thin Places (CaD Ps 48) – Wayfarer
Walk about Zion, go all around it,
count its towers…
Throughout the history of the Jesus Movement and Christendom, there have been various geographic locations around the world that have come to be known as "thin places." The concept is a very simple metaphor. It is a specific location where the divide between temporal and eternal, heaven and earth, matter and Spirit, is thin. The power of the Spirit seems to flow more palpably. "Thin places" might be locations where spiritual revivals have occurred, miracles have occurred, or where people experience God's presence in extraordinary ways.
One of the things I've noticed in moving from Book I of the Psalms (Psalms 1-41) to Book II (Psalms 42-72). The songs in Book 1 are mostly songs of David expressing his personal emotions and faith. In the first six songs of Book II we've had a variety of songs that were written with specific liturgical purposes. There's been a diplomatic wedding of royalty to another nation's princess, a song celebrating a king's enthronement, and a community plea/prayer after suffering military defeat.
Today's chapter, Psalm 48, is a song that celebrates Jerusalem as the center of Hebrew worship. It celebrates Jerusalem as an ancient thin place where people find joy, where God has done great things, where the things of God are pondered, and spiritual guidance is found.
It was very common in ancient Mesopotamian cultures for major cities to have patron deities and temples to those deities. The Hebrews would have experienced this while in slavery in Egypt. They would have been familiar with the concept, and way back during the Hebrews flight from Egypt God made clear that a city would be established as the place where Yahweh would dwell and be worshipped (Deut 12:5). How fascinating that over 3000 years later pilgrims from all over the world continue to flock to Jerusalem and pray at the Western Wall of the temple ruins. It is still considered by many to be a thin place.
In the quiet this morning, Psalm 48 has me thinking about thin places. I have been to Jerusalem, I have walked its streets, and I have prayed at the Western Wall. Personally, I didn't find Jerusalem to be a thin place but a dark place, despite knowing that the Great Story makes clear it still has a role to play in history's climactic events.
I have, however, observed that our place at the lake is what I've experienced as a thin place. It is a place people have found peace. It is a place where both myself and others have found healing of both body and soul. It has been a place of retreat, of soul-searching, of life-changing conversation, of joy, of love, and of Life.
In my spiritual journey, I've come to believe it vital to identify and regularly visit a thin place. I'm reminded that Jesus regularly slipped away alone or with his closest followers to the top of a mountain along the shores of Galilee to pray. Interestingly enough, when I visited that mountain-top location in Israel, I found it to be the thinnest place I personally experienced in my tour of many, many sites in the Holy Land.
This world bombards me ceaselessly with data, information, opinions, advertisements, and pleas for my time, energy, and human resources. My spirit needs a thin place to recharge, even if it's a thin place just to me.
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King of the Mountain
King of the Mountain (CaD Ps 47) – Wayfarer
God is king over the nations;
God sits on his holy throne.
I think that the changing of the seasons brings back certain specific childhood memories. Here in Iowa the last few weeks have ushered in the harsh realities of winter. The snow has already begun to descend. In yesterday's post I was thinking specifically about the memories of walking to-and-from school. This morning, it's snow.
The cool thing for a kid growing up the city in Iowa was the way snow completely transformed the landscape. Not only did it layer everything with this thick blanket of white, but the snowplows and shovels created tiny mountain ranges of snow on every street corner, parking lot, playground, and driveway.
For kids this meant one thing: a game called "King of the Mountain!"
The game is simple. Climb to the top. Stake your claim as King of the Mountain, then get ready to take on all challengers your throne on the mountaintop of ice and snow. Go!! Seriously. Between King of the Mountain, public smoking, the ability for any child to buy cigarettes out of a vending machine, and the fact that seat belts were considered optional accessories that you stuffed into the crack between the seats so they wouldn't poke you…How did we survive childhood in the 1970's?!
Why did my brain go there this morning? Today's chapter is Psalm 47 which was a song of enthronement. In all ancient Mesopotamian cultures the celebration of a king's enthronement was a huge deal. There was a parade, a procession, loud music, an entire nation dancing, clapping, singing…think Kool & the Gang singing "Celebrate good times! Come on!" (Man, now my brain is stuck on Memory Ln.!)
The fascinating thing about this Hebrew song of enthronement is that the metaphor is that of God ascending His holy mountain (for the Hebrews that was Mount Zion where God's temple was located) to be enthroned over all the earth, all the nations, all of creation.
The metaphor of God as king is one that that emerged during the time of the ancient monarchy of the Hebrews. The prophet Isaiah has his famous vision of being taken up into the throne room of God. The theme was written into the liturgical worship songs like Psalm 47. It is carried on through the entirety of the Great Story. The Messiah was pictured as king over the entire earth. After Jesus ascended to heaven, the apostles all referenced Jesus sitting at "the right hand of the Father" in heaven. Paul (who had his own wild vision experience of being taken up into heaven) referred to Jesus as "King of Kings," and he wrote to the followers of Jesus in Phillipi:
Therefore God also highly exalted [Jesus]
and gave him the name
that is above every name,
so that at the name of Jesus
every knee should bend,
in heaven and on earth and under the earth,
and every tongue should confess
that Jesus Christ is Lord,
to the glory of God the Father.
In the book of Revelation, John has a vision of the throne room of heaven where "The Lamb who was slain" sits on the throne.
Enthronement is a big deal in the Great Story, but the metaphor has very personal implications. When I became a follower of Jesus on a frigid Iowa winter night back in 1981, I knew that it was time for me to stop spiritually playing "King of the Mountain" with my own soul. I told Jesus that I was stepping down as king of my own life, and I invited Jesus to be enthroned in my heart and my life. I confess that I haven't always been a perfect subject, but that spiritual reality has never changed for me over the last forty years. I have continually sought to give Jesus dominion on the throne of my life and pursue His purposes for me in this life journey.
And, what's cool is that the metaphor doesn't end there. Having spiritually abdicated and given Jesus the throne of my life, Jesus did not consider me an enemy, a threat, a usurper to be banished from the kingdom and taken out lest I try to take back the throne. No, I get adopted into the royal family. I am given a place, a role, an inheritance, and, in the Great Story, I am now referenced as a "co-heir" with Jesus. I have a place in the procession, at the king's table, in the king's family.
You know what that makes me think?!
[cue: Kool and the Gang]
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redpajama_set_name: RedPajamaCommonCrawl