Maxwell's field coupled nonminimally to quadratic torsion: Induced axion field and birefringence of the vacuum

Abstract

We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^{\alpha }$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F{T}^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2{T}^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can be completely described in the framework of metricfree electrodynamics. We recognize three physical effects generated by the torsion: (i) An axion field that induces an {\em optical activity} into spacetime, (ii) a modification of the light cone structure that yields {\em birefringence} of the vacuum, and (iii) a torsion dependence of the {\em velocity of light.} We study these effects in the background of a Friedmann universe with torsion. {\it File tor17.tex, 02 August 2003}

6 pages