Planar QED in Magnetic or Electric Solitonic Backgrounds

TL;DR

This paper reviews the resolvent technique for calculating the effective action in planar QED, highlighting exact results for certain solitonic backgrounds and their implications for fermion energies and pair creation probabilities.

Contribution

It introduces exact computations of the effective action in specific solitonic backgrounds within planar QED, advancing analytical methods in the field.

Findings

Exact effective actions for certain solitonic backgrounds

Connection between effective action and fermion pair creation

Analytical techniques for static magnetic and electric backgrounds

Abstract

We review the resolvent technique for computing the effective action in planar QED. For static magnetic backgrounds the effective action yields (minus) the effective energy of the fermions, while for electric backgrounds the imaginary part of the effective action gives (half) the probability of fermion-antifermion pair creation. For some special `solitonic' background profiles, these effective actions can be computed exactly.