Related papers: New integrable two-centre problem on sphere in Dir…
The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of…
We construct a two-dimensional family of integrable coupled Dirac--scalar field theories in $1+1$ dimensions, parameterized by $(\thz,\alpha)\in[0,\pi/2]^2$, whose Lax connection takes values in $\slC$ throughout. The family arises as the…
In this note we generalized the Dirac non-linear electrodynamics, by introducing two potentials (namely, the vector potential A and the pseudo-vector potential gamma^5 B of the electromagnetic theory with charges and magnetic monopoles) and…
The motion of compressible, inviscid fluid under the constant pressure on a rotating sphere is studied. The hodograph equations for the corresponding Euler equation are presented. They provide us with the class of solutions of the Euler…
Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems. This model, however, does not belong to the classes based on the algebra…
The magnetization for electrons on a two-dimensional sphere, under a spherically symmetrical normal magnetic field has been studied in the large field limit. This allows us to use an Euclidean approximation for low energies electron states…
Aspects of three dimensional $\mathcal{N}=2$ gauge theories with monopole superpotentials and their dualities are investigated. The moduli spaces of a number of such theories are studied using Hilbert series. Moreover, we propose new…
In this paper we correct previous work on magnetic charge plus a photon mass. We show that contrary to previous claims this system has a very simple, closed form solution which is the Dirac string potential multiplied by a exponential…
With two typical parent actions we have two kinds of dual worlds: i) one of which contains an electric as well as magnetic current, and ii) the other contains (generalized) Chern-Simons terms. All these fields are defined on a curved…
A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping…
We extend Dirac's `extensible model of the electron' to include spin and family. $U(1)_{e.m.}$ charge conservation on the bubble is translated into a secondary $U(1)_{g}$ world-manifold gauge principle. Reflecting the secondary magnetic…
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
We propose a new vector potential for the Abelian magnetic monopole. The potential is non-singular in the entire region around the monopole. We argue how the Dirac quantization condition can be derived for any choice of potential.
We present a steady Euler flow on the round 3-sphere whose velocity vector field has the property of having two independent first integrals, being tangent to the fibres of an almost submersion onto the 2-sphere. This submersion turns out to…
We show that the one dimensional unitary matrix model with potential of the form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
Cubic invariants for two-dimensional degenerate Hamiltonian systems are considered by using variables of separation of the associated St\"ackel problems with quadratic integrals of motion. For the superintegrable St\"ackel systems the cubic…
The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a…
The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…