Spinor Covariant Derivative on Degenerate Manifolds

In this work, we define a spinor covariant derivative for degenerate manifolds with 4-dimensions. To perform this, we have found the principal bundle by using a degenerate spin group. Then, we benefit from a covering map to establish a relationship between the local connection forms of principal bun...

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Bibliographic Details
Published in:Reports on mathematical physics 2020-10, Vol.86 (2), p.241-262
Main Authors: Şekercı, Gülşah Aydin, Çöken, Abdılkadır Ceylan
Format: Article
Language:English
Subjects:
Clifford algebras
fiber bundles
Lorentz metrics
spin geometry
spin manifold
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Summary:In this work, we define a spinor covariant derivative for degenerate manifolds with 4-dimensions. To perform this, we have found the principal bundle by using a degenerate spin group. Then, we benefit from a covering map to establish a relationship between the local connection forms of principal bundles. After that, we define a covariant derivative on a degenerate spinor bundle which is an associated bundle.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(20)30074-4