Date of Award

Spring 1-1-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Alexander Gorokhovsky

Second Advisor

Carla Farsi

Third Advisor

Vijay K. Gupta

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.

Included in

Mathematics Commons

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