On the definition of geometric Dirac operators

Details On the definition of geometric Dirac operators On the definition of geometric Dirac operators

2000-05-24

arxiv.org/abs/math/0005239v1

Mathematics

Differential Geometry

40 pages, LaTex2e

Scientific paper

In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define (and characterize) spin structures and the corresponding Spin-Dirac operator purely in the spirit of irreducible representations. We also prove its equivalence with the usual approach via principal bundles. We conclude with other geometric Dirac operators and their properties using the afore-mentioned setting.

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