The construction of spinor fields on manifolds with smooth degenerate metrics

Schray, Jörg and Dray, Tevian and Manogue, Corinne A. and Tucker, Robin and Wang, Charles (1996) The construction of spinor fields on manifolds with smooth degenerate metrics. Journal of Mathematical Physics, 37 (8). pp. 3882-3897. ISSN 0022-2488

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Abstract

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 express‐ ion 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.

Item Type: Journal Article
Journal or Publication Title: Journal of Mathematical Physics
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/3100/3109
Subjects:
Departments: Faculty of Science and Technology > Physics
ID Code: 75080
Deposited By: ep_importer_pure
Deposited On: 07 Aug 2015 14:36
Refereed?: Yes
Published?: Published
Last Modified: 30 Sep 2019 18:41
URI: https://eprints.lancs.ac.uk/id/eprint/75080

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