Effective Energy for QED$_{2+1}$ with Semi-Localized Static Magnetic Fields: A Solvable Model

TL;DR

This paper computes the exact effective energy in 2+1 dimensional QED with semi-localized magnetic fields, revealing relations in the derivative expansion and showing the uniform field minimizes energy at fixed flux.

Contribution

It provides an exact solution for the effective energy in a solvable model of QED$_{2+1}$ with localized magnetic fields, connecting to derivative expansion relations.

Findings

Exact effective energy expression derived.

Relations between derivative expansion terms established.

Uniform magnetic field minimizes energy at fixed flux.

Abstract

We evaluate the exact ${\rm QED}_{2+1}$ effective energy for charged spin zero and spin half fields in the presence of a family of static magnetic field profiles localized in a strip of width $\lambda$. The exact result yields an infinite set of relations between the terms in the derivative expansion of the effective energy for a general magnetic field. Upon addition of the standard Maxwell magneto-static energy, the minimum energy configuration at fixed flux corresponds to a uniform magnetic field.