Graduate Thesis Or Dissertation

 

Getzler Symbol Calculus via Deformation Quantization Public Deposited

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https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/gh93gz52t
Abstract
  • Two quantization methods are considered on the cotangent bundle of a Riemannian manifold. Namely, Fedosov's deformation quantization on a symplectic manifold and Getzler's pseudodierential symbol calculus with fermionic variables, which is used to simplify the proof of the Atiyah-Singer index theorem for the Dirac operator on a spin manifold. We show how to introduce fermionic variables in Fedosov's construction and obtain a deformation that is analogous to Getzler's symbol calculus on the cotangent bundle of a given Riemannian manifold.
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  • 2012
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  • 2019-11-16
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