New exactly solvable relativistic models with anomalous interaction

TL;DR

This paper introduces a new exactly solvable relativistic model describing anomalous interactions of a neutral Dirac fermion with a cylindrically symmetric electromagnetic field, extending known non-relativistic models.

Contribution

It presents a novel relativistic Dirac-Pauli model with an external field combining electric and magnetic components, which reduces to the Pron'ko-Stroganov model in the non-relativistic limit.

Findings

Derivation of an exactly solvable relativistic Dirac model.

Connection to the Pron'ko-Stroganov model in the non-relativistic limit.

Explicit form of the external electromagnetic field.

Abstract

A special class of Dirac-Pauli equations with time-like vector potentials of external field is investigated. A new exactly solvable relativistic model describing anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external e.m. field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In non-relativistic approximation the considered model is reduced to the integrable Pron'ko-Stroganov model.