Related papers: Electrostatic problems with a rational constraint …
A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…
We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition…
This work deals with an Abelian gauge field in the presence of an electric charge immersed in a medium controlled by neutral scalar fields, which interact with the gauge field through a generalized dielectric function. We develop an…
The theory of orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to functional-difference…
We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor…
The dynamics of the electrons for a molecule in solution is coupled to the dynamics of its polarizable environment, i.e., the solvent. To theoretically investigate such electronic dynamics, we have recently developed equations of motion…
We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the…
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the…
Based on the motivation of generalizing the correspondence between the Lax equation for the Toda lattice and the deformation theory of the orthogonal polynomials, we derive a q-deformed version of the Toda equations for both…
We provide sufficient conditions for the existence of periodic solutions of the of the Lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. The basic assumptions cover relevant…
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of…
We obtain classical solutions of $\l$-deformed $\s$-models based on $SL(2,\mathbb{R})/U(1)$ and $SU(2)/U(1)$ coset manifolds. Using two different sets of coordinates, we derive two distinct classes of solutions. The first class is expressed…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
The dynamic $U (1)$ symmetry of classical electrodynamics without charges, similar to the known phase symmetry of quantum mechanics, is analyzed. Using this symmetry, alternative Lagrangians of classical electrodynamics, similar to…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
We find an exact solution to the charged 2-body problem in $(1+1)$ dimensional lineal gravity which provides the first example of a relativistic system that generalizes the Majumdar-Papapetrou condition for static balance.
In this paper, we compute universal estimates of eigenvalues for a class of coupled systems of elliptic differential equations in divergence form on a bounded domain in Euclidean space, which includes the well-known Lam\'e and the Laplacian…
A $\mathbb{D}$-semi-classical weight is one which satisfies a particular linear, first order homogeneous equation in a divided-difference operator $\mathbb{D}$. It is known that the system of polynomials, orthogonal with respect to this…
The multivariable version of ordinary and generalized Hermite polynomials are the natural solutions of the classical heat equation and of its higher order versions. We derive the associated Burgers equations and show that analogous…
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation $[\hat P,\hat M]=1$. In ordinary quantum mechanics $\hat P$ is the derivative and $\hat M$ the coordinate operator. Here we shall realize $\hat P$ as…