Analytic results for the effective action

TL;DR

This paper derives explicit formulas for the one-loop effective action in constant electromagnetic fields across various dimensions, covering both massive and massless particles, and discusses their limits using zeta function renormalization.

Contribution

It provides closed-form expressions for the effective action in multiple dimensions and clarifies the connection to Schwinger's original work using zeta function techniques.

Findings

Explicit formulas for effective action in 2D, 3D, 4D

Analysis of strong and weak field limits

Connection to Euler-Heisenberg Lagrangian

Abstract

Motivated by the seminal work of Schwinger, we obtain explicit closed form expressions for the one-loop effective action in a constant electromagnetic field. We discuss both massive and massless charged scalars and spinors in two, three, and four dimensions. Both strong field and weak field limits are calculable. The latter limit results in an asymptotic expansion whose first term reproduces the Euler-Heisenberg effective Lagrangian. We use the zeta function renormalization prescription, and indicate its relationship to Schwinger's renormalized effective action.