Scalar and Spinor Fields in Signature Changing Spacetimes

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.