The Spin-c Dirac Operator

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


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.


Dirac Operator Principal Bundle Local Frame Principal Symbol Covariant Differentiation 
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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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