The Spin-c Dirac Operator
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.
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