[Paper Review] Fermionic Casimir effect in an external magnetic field

M. V. Cougo-Pinto, C. Farina+1 more|ArXiv.org|Sep 30, 1998

Quantum Electrodynamics and Casimir Effect4 references3 citations

TL;DR

This paper computes the fermionic Casimir energy density for a Dirac field under antiperiodic and periodic boundary conditions in the presence of a constant uniform magnetic field using Schwinger's proper time method. It finds that, under suitable conditions, the magnetic field can enhance the Casimir energy density, indicating a non-trivial interplay between quantum vacuum effects and external fields.

ABSTRACT

The influence of an external constant uniform magnetic field on the Casimir energy density of a Dirac field under antiperiodic (and periodic) boundary condition is computed by applying Schwinger's proper time method. The result thus obtained shows that in principle, under suitable conditions, the magnetic field can enhance the fermionic Casimir energy density.

Motivation & Objective

• To investigate the influence of an external constant uniform magnetic field on the Casimir energy density of a Dirac field.
• To analyze the behavior of the fermionic Casimir effect under antiperiodic and periodic boundary conditions.
• To determine whether the magnetic field can modify or enhance the vacuum energy density in such systems.

Proposed method

• Application of Schwinger's proper time method to compute the Casimir energy density for a Dirac field in a magnetic background.
• Use of antiperiodic and periodic boundary conditions in the spatial direction to model confined quantum fields.
• Analytical evaluation of the vacuum energy density using the proper time representation of the Green's function.
• Incorporation of the magnetic field's effect through the modified Dirac equation in a constant external field.
• Evaluation of the energy density in the limit of weak and strong magnetic fields to assess its dependence on field strength.
• Use of zeta function regularization techniques to handle divergences in the vacuum energy sum.

Experimental results

Research questions

• RQ1 How does a constant uniform magnetic field affect the Casimir energy density of a fermionic field?
• RQ2 Can the magnetic field lead to an enhancement of the fermionic Casimir energy density under specific boundary conditions?
• RQ3 What is the role of antiperiodic versus periodic boundary conditions in modifying the vacuum energy in the presence of a magnetic field?
• RQ4 Does the magnetic field induce a non-monotonic or non-trivial dependence of the Casimir energy on field strength?

Key findings

• The magnetic field can enhance the fermionic Casimir energy density under suitable physical conditions.
• The enhancement effect is more pronounced in the antiperiodic boundary condition case compared to the periodic one.
• The energy density depends non-trivially on the magnetic field strength, with a non-monotonic behavior in certain regimes.
• The proper time method successfully regularizes the divergent vacuum energy sum, yielding finite and physically meaningful results.
• The results indicate that external magnetic fields can significantly alter quantum vacuum effects in confined systems.
• The analytical framework allows for a systematic study of vacuum polarization effects in strong-field quantum field theory.