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The Spin-c Dirac Operator

  • J. J. Duistermaat
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In this chapter we start by viewing E as a principal bundle for the group Spinc (2n), which contains the unitary group. The fact that Spinc (2n) also contains the spin group Spin(2n), which is a twofold cover of SO(2n), allows us to introduce a connection in this principal bundle which has the desired compatibility with the Levi-Civita connection. Using this connection in E, we will give the definition of the spin-c Dirac operator D in (5.14). In Lemma 5.5 it is established that D is selfadjoint and has the same principal symbol as the Dolbeault-Dirac operator.

Keywords

Dirac Operator Principal Bundle Local Frame Principal Symbol Covariant Differentiation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • J. J. Duistermaat
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

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