Date of Award
Doctor of Philosophy (PhD)
Vijay K. Gupta
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.
Mesa, Camilo, "Getzler Symbol Calculus via Deformation Quantization" (2012). Mathematics Graduate Theses & Dissertations. 14.