Kleinian signature change

Abstract

We study the propagation of plane-waves in a fixed flat background spacetime whose metric changes from a Lorentzian signature to a Kleinian signature . When the change of signature is discontinuous there is an apparent difference in wave behaviour depending upon whether the wave describes matter with integer or half-integer spin. A more detailed study of the Dirac equation shows that, while it is possible to decrease this disparity, the two matter classes still do not behave identically. A more consistent picture finally emerges when the same problem is attempted with a metric which changes signature continuously. This leads to the prediction of some surprising physical phenomena.