Confined quantum fields under the influence of a uniform magnetic field

TL;DR

This paper studies how a uniform magnetic field affects the zero-point energy of charged scalar and fermion fields with specific boundary conditions, providing exact, analytical, and numerical results.

Contribution

It offers exact solutions for scalar fields and analytical limits for fermion fields under magnetic influence, including numerical analysis for complex cases.

Findings

Exact results for scalar fields under magnetic fields.

Analytical limits for fermion fields at small and large masses.

Numerical analysis confirming theoretical results.

Abstract

We investigate the influence of a uniform magnetic field on the zero-point energy of charged fields of two types, namely, a massive charged scalar field under Dirichlet boundary conditions and a massive fermion field under MIT boundary conditions. For the first, exact results are obtained, in terms of exponentially convergent functions, and for the second, the limits for small and for large mass are analytically obtained too. Coincidence with previously known, partial result serves as a check of the procedure. For the general case in the second situation --a rather involved one-- a precise numerical analysis is performed.