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.
Recommended Citation
Mesa, Camilo, "Getzler Symbol Calculus via Deformation Quantization" (2012). Mathematics Graduate Theses & Dissertations. 14.
https://scholar.colorado.edu/math_gradetds/14