THE CONSTRUCTION OF SPINOR FIELDS ON MANIFOLDS WITH SMOOTH DEGENERATEMETRICS

We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hyperface that partition s the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex spinor fibration to make precise the meaning of c ontinuity of a spinor field and give an expression for the components of a local spinor connection that is valid in the absence of a frame o f local orthonormal vectors. These considerations enable one to constr uct a Dirac equation for the discussion of the behavior of spinors in the vicinity of the metric degeneracy. We conclude that the theory con tains more freedom than the spacetime Dirac theory and we discuss some of the implications of this for the continuity of conserved currents. (C) 1996 American Institute of Physics.