Introductory Notes on Non-linear Electrodynamics and its Applications

TL;DR

This paper reviews the development, properties, and applications of non-linear electrodynamics, highlighting models with special symmetries and their implications in physics, cosmology, and material science.

Contribution

It provides an overview of various non-linear electrodynamics models, emphasizing recent conformal and duality-invariant modifications and their physical significance.

Findings

Non-linear electrodynamics models exhibit unique symmetries like conformal invariance.

Applications include phenomena such as vacuum birefringence and charged black holes.

Holographic approaches connect these models to condensed matter properties.

Abstract

In 1933-1934 Born and Infeld constructed the first non-linear generalization of Maxwell's electrodynamics that turned out to be a remarkable theory in many respects. In 1935 Heisenberg and Euler computed a complete effective action describing non-linear corrections to Maxwell's theory due to quantum electron-positron one-loop effects. Since then, these and a variety of other models of non-linear electrodynamics proposed in the course of decades have been extensively studied and used in a wide range of areas of theoretical physics including string theory, gravity, cosmology and condensed matter (CMT). In these notes I will overview general properties of non-linear electrodynamics and particular models which are distinguished by their symmetries and physical properties, such as a recently discovered unique non-linear modification of Maxwell's electrodynamics which is conformal and duality invariant. I will also sketch how non-linear electromagnetic effects may manifest themselves in physical phenomena (such as vacuum birefringence), in properties of gravitational objects (e.g. charged black holes) and in the evolution of the universe, and can be used, via gravity/CMT holography, for the description of properties of certain conducting and insulating materials.