J. Schray et al., THE CONSTRUCTION OF SPINOR FIELDS ON MANIFOLDS WITH SMOOTH DEGENERATEMETRICS, Journal of mathematical physics, 37(8), 1996, pp. 3882-3896
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.