Connections on Clifford bundles and the Dirac operator
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.
scientific article; zbMATH DE number 4050601
scientific article