Related papers: Integrable generalisations of Dirac magnetic monop…
In this paper we present the construction of all nonstandard integrable systems in magnetic fields whose integrals have leading order structure corresponding to the case (i) of Theorem 1 in [A Marchesiello and L \v{S}nobl 2022 {\it J. Phys.…
Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear…
In a previous paper, we found an extension of the N-dimensional Lorentz generators that partially restores the closed operator algebra in the presence of a Maxwell field, and is conserved under system evolution. Generalizing the…
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate…
The families index theory for the overlap lattice Dirac operator is applied to derive topological features of the space of SU(N) lattice gauge fields on the 4-torus: The topological sectors, specified by the fermionic topological charge,…
We generalize our discussions and give more general physical applications of a new solution to the strong CP problem with magnetic monopoles as originally proposed by the author$^1$. Especially, we will discuss about the global topological…
We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to…
As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two…
We study the Moffatt's magnetic relaxation equation with Darcy-type regularization for the constitutive law. This is a topology-preserving dissipative equation, whose solutions are conjectured to converge in the infinite time limit towards…
We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second class constraints the Dirac brackets of the proposed theory represent the commutation relations for…
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
The model of magnetic monopoles that was proposed by Paul Dirac in 1931 has long been a subject of theoretical interest in physics because of its potential to explain the quantization of electric charge. While much attention has been given…
We consider motion of a material point placed in a constant homogeneous magnetic field in $\mathbb R^n$ and also motion restricted to the sphere $S^{n-1}$. While there is an obvious integrability of the magnetic system in $\mathbb R^n$, the…
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 discuss the generalization of Abelian Chern-Simons theories when $\theta $-angles and magnetic monopoles are included. We map sectors of two dimensional Conformal Field Theories into these three dimensional theories.
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…
The close connection of electricity and magnetism is one of the cornerstones of modern physics. This connection plays crucial role from the fundamental point of view and in practical applications, including spintronics and multiferroic…
Topological semimetals, representing a new topological phase that lacks a full bandgap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a…
Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a…
Dirac showed that the existence of one magnetic pole in the universe could offer an explanation of the discrete nature of the electric charge. Magnetic poles appear naturally in most grand unified theories. Their discovery would be of…