Divergences in the effective action for acausal spacetimes

Abstract

The 1-loop effective Lagrangian for a massive scalar field on an arbitrary causality violating spacetime is calculated using the methods of Euclidean quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and twisted field configurations are also considered. In general, we find that the Lagrangian diverges to minus infinity at each of the nth polarized hypersurfaces of the spacetime with a structure governed by a DeWitt - Schwinger type expansion.