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For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
The general classical equation of spin motion is rigorously derived for a particle with electric and magnetic charges and dipole moments in electromagnetic fields. The equation describing the spin motion relative to the momentum direction…
Dedicated to Ludwig Faddeev on his 80th birthday. Ludwig exemplifies perfectly a mathematical physicist: significant contribution to mathematics (algebraic properties of integrable systems) and physics (quantum field theory). In this note I…
As one of the most elegant theories in physics, Yang-Mills (YM) theory not only incorporates Maxwell's equations unifying electromagnetism, but also underpins the standard model explaining the electroweak and strong interactions in a…
We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.
Some relations between conformal relativity and Weyl-Dirac theory are rephrased and clarified.
We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions…
This article was published as Sec.5 of the "Roadmap on Structured Light" in Journal of Optics 19 (2017) 013001. Section 5 describes the essential elements of the classical theory of electromagnetic angular momentum.
We review recent advances in the numerical analysis of the Monge-Amp\`ere equation. Various computational techniques are discussed including wide-stencil finite difference schemes, two-scaled methods, finite element methods, and methods…
I give a brief introduction to the relation between loop quantum gravity and twistor theory, and comment on some perspectives on the problem of time.
The purpose of this work is to retrace the steps that were made by scientists of XX century, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two…
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
This is a Reply to the Comment [arXiv:0807.0699] on our paper [PRL 100:232002 (2008)].
This paper follows up a recent debate as to whether classical electrodynamics is inconsistent. I suggest that disagreements can be managed by disambiguating 'theory' in two different ways.
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
We solve the weighted energy problem on the unit circle, by finding the extremal measure and describing its support. Applications to polynomial and exponential weights are also included.
Contribution to the Proceedings of the International Congress of Mathematicians 1994. We review recent developments in the physics and mathematics of Yang-Mills theory in two dimensional spacetimes. This is a condensed version of a…
The equations of motion of quantum Yang - Mills theory (in the planar `large N' limit), when formulated in Loop-space are shown to have an anomalous term, which makes them analogous to the equations of motion of WZW models. The anomaly is…