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-Cevita connection (or Kaehler-Dirac operator) over the finite group generated by an orthonormal frame of thebase manifold. The familiar convariance 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. (orig.)