Nonlinear Electrodynamics and QED

TL;DR

This paper reviews the transition from linear to nonlinear electrodynamics, emphasizing the role of quantum electrodynamics' empirical successes in guiding theoretical extensions and exploring related phenomena like nonlinear optics.

Contribution

It synthesizes classical nonlinear electrodynamics theories with modern geometric methods and discusses how spacetime topology influences electromagnetic behavior.

Findings

Established nonlinear theories like Mie, Born, and Infeld are presented.

Spacetime curvature and topology can modify electromagnetic phenomena.

Nonlinear optics offers insights into extending electrodynamics nonlinearly.

Abstract

The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topological methods of mathematical physics. The manner by which spacetime curvature and topology can affect electromagnetism is also reviewed. Finally, the phenomena of nonlinear optics are discussed as a possible guide to building one's intuition regarding the process of extending electrodynamics into nonlinearity in a manner that is consistent with the qualitative and empirical results of quantum electrodynamics.