Connections on Clifford bundles and the Dirac operator
type: Item
instance of: scholarly article
title: Connections on Clifford bundles and the Dirac operator
zbMATH Open document ID: 0644.58028
DOI: 10.1007/BF00570772
published in: Letters in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: It is shown, how, in the setting of Clifford bundles, the spin connection (or Dirac operator) may be obtained by averaging the Levi-Civita connection (or Kähler-Dirac operator) over the finite group generated by an orthonormal frame of the base manifold. The familiar covariance of the Dirac equation under a simultaneous transformation of spinors and matrix representations emerges very naturally in this scheme, which can also be applied when the manifold does not possess a spin structure.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 55R10
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 4050601
zbMATH Keywords: Clifford bundles
zbMATH Keywords: spin connection
zbMATH Keywords: Dirac operator
zbMATH Keywords: Levi-Civita connection
zbMATH Keywords: Kähler-Dirac operator
author: Matthias Blau
MaRDI profile type: Publication
cites work: Fermions without spinors
cites work: The Dirac equation in exterior form
cites work: Multilinear algebra. 2nd ed
cites work: Spinors in n Dimensions
cites work: Q5830680
cites work: Q4102494
cites work: Ideal-preserving Lorentzian connections
cites work: Realization, extension, and classification of certain physically important groups and algebras
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description: scientific article; zbMATH DE number 4050601