Heisenberg-Euler Effective Lagrangians : Basics and Extensions

TL;DR

This paper provides a comprehensive pedagogical review of Heisenberg-Euler effective Lagrangians, covering foundational concepts, key applications, and recent extensions to complex background fields and higher loop calculations.

Contribution

It offers a detailed overview of the original and extended formulations of effective Lagrangians in quantum electrodynamics, emphasizing pedagogical clarity and recent developments.

Findings

Summarizes the original Heisenberg-Euler and Weisskopf work.

Discusses extensions to inhomogeneous and nonabelian backgrounds.

Highlights progress in higher loop effective Lagrangians.

Abstract

I present a pedagogical review of Heisenberg-Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important applications and generalizations to inhomogeneous background fields, nonabelian backgrounds, and higher loop effective Lagrangians.