Faraday effect : a field theoretical point of view

TL;DR

This paper investigates the vacuum polarization tensor in electromagnetic fields, revealing how Faraday rotation is affected by medium degeneracy and relativistic conditions, with explicit formulas provided.

Contribution

It introduces a symmetry-based analysis of the vacuum polarization tensor and derives modified Faraday rotation expressions for degenerate and relativistic media.

Findings

Faraday rotation is modified in degenerate and relativistic media.

Symmetry arguments constrain the form of the vacuum polarization tensor.

Explicit formulas for Faraday rotation in extreme media are provided.

Abstract

We analyze the structure of the vacuum polarization tensor in the presence of a background electromagnetic field in a medium. We use various discrete symmetries and crossing symmetry to constrain the form factors obtained for the most general case. From these symmetry arguments, we show why the vacuum polarization tensor has to be even in the background field when there is no background medium. Taking then the background field to be purely magnetic, we evaluate the vacuum polarization to linear order in it. The result shows the phenomenon of Faraday rotation, i.e., the rotation of the plane of polarization of a plane polarized light passing through this background. We find that the usual expression for Faraday rotation, which is derived for a non-degenerate plasma in the non-relativistic approximation, undergoes substantial modification if the background is degenerate and/or relativistic. We give explicit expressions for Faraday rotation in completely degenerate and ultra-relativistic media.