Vacuum energies for the relativistic Landau problem

TL;DR

This paper uses zeta-function methods to analyze vacuum energies of Dirac fields in a magnetic background, considering boundary conditions and charge renormalization effects.

Contribution

It introduces a detailed zeta-function approach to compute vacuum energies with various boundary conditions in a relativistic Landau problem.

Findings

Vacuum energies depend on boundary conditions and magnetic field strength.

Charge renormalization is essential for consistent energy calculations.

The method provides a systematic way to evaluate quantum vacuum effects in magnetic backgrounds.

Abstract

We study, through zeta-function techniques, the vacuum energies for Dirac fields in a constant magnetic background. We consider the combined effect of the background and twisted boundary conditions. The required charge renormalization is discussed in each case.