Scalar and spinor fields in signature-changing spacetimes

The propagation of scalar and spinor fields in a spacetime whose metric changes signature is analyzed. The recent work of Dray, Manogue, and Tucker 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-1/2 field. In contrast with 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.