Magnetic Permeability of Constrained Fermionic Vacuum

TL;DR

This paper calculates the magnetic permeability of a fermionic vacuum with one spatial dimension compactified into a circle, revealing a novel contribution that is negligible in typical laboratory settings but potentially significant in strong interaction contexts.

Contribution

It introduces a new contribution to vacuum permeability arising from fermion fluctuations in a compactified dimension using Schwinger's proper time method.

Findings

Identifies a novel contribution to vacuum permeability.

Contributions are negligible for typical laboratory cavity sizes.

Potential relevance in strong interaction physics.

Abstract

We obtain using Schwinger's proper time approach the Casimir-Euler-Heisenberg effective action of fermion fluctuations for the case of an applied magnetic field. We implement here the compactification of one space dimension into a circle through anti-periodic boundary condition. Aside of higher order non-linear field effects we identify a novel contribution to the vacuum permeability. These contributions are exceedingly small for normal electromagnetism due to the smallness of the electron Compton wavelength compared to the size of the compactified dimension, if we take the latter as the typical size of laboratory cavities, but their presence is thought provoking, also considering the context of strong interactions.