Divergences in the Effective Action for Acausal Spacetimes

TL;DR

This paper calculates the one-loop effective Lagrangian for various quantum fields in causality-violating spacetimes, revealing divergences at polarised hypersurfaces, which has implications for quantum field theory in such backgrounds.

Contribution

It extends the calculation of the effective Lagrangian to acausal spacetimes and includes different field spins and twisted configurations, highlighting divergence structures.

Findings

Lagrangian diverges to minus infinity at polarised hypersurfaces

Divergences follow a DeWitt-Schwinger type expansion

Results apply to scalar, spinor, vector, and twisted fields

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 polarised hypersurfaces of the spacetime with a structure governed by a DeWitt-Schwinger type expansion.