Faraday effect : A field theoretical point of view

Abstract

We analyze the structure of the vacuum polarization tensor in the presence of a background electromagnetic field in a medium. The most general gauge invariant structure contains many form factors. We use various discrete symmetries and crossing symmetry to constrain these form factors. 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. Finally, we calculate the amount of Faraday rotation in different kinds of media - non-relativistic, completely degenerate, and ultra-relativistic.