Casimir effect in external magnetic field

TL;DR

This paper investigates how external magnetic fields influence the Casimir effect for charged scalar and Dirac fields, calculating vacuum energies through canonical formalism and mode summation, with renormalization via the Abel-Plana formula.

Contribution

It provides a detailed analysis of the Casimir effect for charged fields in magnetic fields using canonical formalism and mode summation, including renormalization techniques.

Findings

Vacuum energy expressions for scalar and Dirac fields in magnetic fields

Application of Abel-Plana formula for renormalization

Insights into magnetic field effects on Casimir energy

Abstract

In this paper we examine the Casimir effect for charged fields in presence of external magnetic field. We consider scalar field (connected with spinless particles) and the Dirac field (connected with 1/2-spin particles). In both cases we describe quantum field using the canonical formalism. We obtain vacuum energy by direct solving field equations and using the mode summation method. In order to compute the renormalized vacuum energy we use the Abel-Plana formula.