Lorentz-violating effects in the spin-1/2 Aharonov-Casher problem

TL;DR

This paper investigates how a Lorentz-violating background affects the Aharonov-Casher effect, revealing modifications in bound states, scattering, and helicity conservation using self-adjoint extension methods.

Contribution

It introduces a novel analysis of Lorentz-violating effects on the Aharonov-Casher problem, deriving explicit formulas for bound states and scattering parameters.

Findings

Additional scattering occurs for all self-adjoint extension parameters.

Bound states exist for negative self-adjoint extension parameters.

Helicity is not conserved in the Lorentz-violating scenario.

Abstract

The effects of a Lorentz symmetry violating background vector on the Aharonov-Casher bound and scattering scenarios is considered. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter. We found that there is an additional scattering for any value of the self-adjoint extension parameter and bound states for negative values of this parameter. By comparing the bound state and scattering results the self-adjoint extension parameter is determined. Expressions for the bound state energies, phase-shift and the scattering matrix are explicitly determined in terms of the self-adjoint extension parameter. The expression obtained for the scattering amplitude reveals that the helicity is not conserved in this scenario.