Scalar and Spinor Fields in Signature Changing Spacetimes

TL;DR

This paper investigates how scalar and spinor fields behave in spacetimes with changing metric signature, highlighting differences in conservation properties and extending previous scalar field analyses to spin-half fields.

Contribution

It extends the analysis of signature change effects from scalar fields to spin-half fields, showing the lack of a conserved inner product for Dirac spinors in such spacetimes.

Findings

Scalar fields exhibit particle production at signature change.

No conserved inner product exists for spin-half fields in signature changing spacetimes.

Different Dirac equations do not yield conserved inner products.

Abstract

The propagation of scalar and spinor fields in a spacetime whose metric changes signature is analyzed. Recent work of Dray et al. on particle production from signature change for a (massless) scalar field is reviewed, and an attempt is made to extend their analysis to the case of a (massless) spin-half field. In contrast to their results for a scalar field, it is shown here---for $SL(2,C)$ spinors---that although there are inequivalent forms of the Dirac equation that can be used to propagate a spinor in a signature changing spacetime, none of these forms gives rise to a conserved inner product on the space of solutions to the field equations.