Vacuum polarization from confined fermions in 3 + 1 dimensions

TL;DR

This paper investigates the one-loop vacuum polarization in massless spinor QED4 confined within a slab with boundary conditions, analyzing induced charges, currents, and effective actions under external electric fields.

Contribution

It provides a detailed analysis of vacuum polarization effects in confined fermions with boundary conditions, including induced charge densities and boundary-dependent effective actions.

Findings

Induced charge density and current profiles due to external electric fields.

Boundary conditions significantly affect vacuum polarization properties.

Identification of epsilon-dependent contributions to the effective action.

Abstract

We study the main properties of the one-loop vacuum polarization function for massless spinor QED4 in a slab, namely, with fields defined on M in R^(3+1), such that M = {(x0, ..., x3)|0 <= x3 <= epsilon}, and bag-like boundary conditions on the boundary. We evaluate the induced charge density and current due to an external constant electric field normal to the boundary; we also study the effective action for a purely transverse field, identifying its epsilon-dependent contribution.