Related papers: Equilibrium of charges and differential equations …
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems…
The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that…
We discuss the similarity of the constituent monopoles of calorons and stable topological solitons with long range Coulombic interaction, classical solutions of the model of topological particles. In the interpretation as electric charges…
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 study solutions to conformally invariant equations with isolated singularties.
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated.We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium…
Dilogarithm identities for the central charges and conformal dimensions exist for at least large classes of rational conformally invariant quantum field theories in two dimensions. In many cases, proofs are not yet known but the numerical…
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…
In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides a rigorous framework for estimating the complexity of solving a system of polynomial equations via Groebner bases…
We consider the algebra associated to a group of transformations which are symmetries of a regular mechanical system (i.e. system free of constraints). For time dependent coordinate transformations we show that a central extension may…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
The path integral of the relativistic Coulomb system is solved, and the wave functions are extracted from the resulting amplitude.
Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and continues to attract significant international attention. This…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
We present explicit expressions for multi-fold logarithmic integrals that are equivalent to sums over polygamma functions at integer argument. Such relations find application in perturbative quantum field theory, quantum chemistry, analytic…
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…
With the sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the equilibrium measure in the presence of an external field…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…