Influence of a magnetic fluxon on the vacuum energy of quantum fields confined by a bag

TL;DR

This paper investigates how magnetic fluxons and boundary conditions affect vacuum energies in quantum fields, using advanced mathematical techniques to compute the Casimir effect in various geometries.

Contribution

It introduces a comprehensive analysis of vacuum energies influenced by magnetic fluxons and boundary conditions, employing zeta-function regularization and Bessel zeta functions.

Findings

Calculated vacuum zero-point energies for bosons and fermions in different geometries.

Applied generalized cut-off regularization and zeta-function techniques.

Provided insights into the Casimir effect under combined boundary and magnetic influences.

Abstract

We study the simultaneous influence of boundary conditions and external fields on quantum fluctuations by considering vacuum zero-point energies for quantum fields in the presence of a magnetic fluxon confined by a bag, circular and spherical for bosons and circular for fermions. The Casimir effect is calculated in a generalized cut-off regularization after applying zeta-function techniques to eigenmode sums and using recent techniques about Bessel zeta functions at negative arguments.