The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics

Details The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics

1996-05-17

arxiv.org/abs/gr-qc/9605037v1

J.Math.Phys. 37 (1996) 3882-3896

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, LaTeX (RevTeX 3.0, no figures), To appear in J. Math. Phys

Scientific paper

10.1063/1.531607

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 hypersurface that partitions the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex spinor fibration to make precise the meaning of continuity 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 of local orthonormal vectors. These considerations enable one to construct a Dirac equation for the discussion of the behavior of spinors in the vicinity of the metric degeneracy. We conclude that the theory contains more freedom than the spacetime Dirac theory and we discuss some of the implications of this for the continuity of conserved currents.

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