Poisson sigma models, reduction and nonlinear gauge theories
Open Access
Author:
Signori, Daniele
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
July 20, 2009
Committee Members:
Ping Xu, Dissertation Advisor/Co-Advisor Ping Xu, Committee Chair/Co-Chair Adrian Ocneanu, Committee Chair/Co-Chair Mathieu Philippe Stienon, Committee Member Luen Chau Li, Committee Member Martin Bojowald, Committee Member Alberto Cattaneo, Committee Member
This dissertation comprises two main lines of research.
Firstly, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories.
Secondly, we give a field theoretic interpretation of the of the BRST (Becchi-Rouet-Stora-Tyutin) and BFV (Batalin-Fradkin-Vilkovisky) methods for the reduction of coisotropic submanifolds of Poisson manifolds. The generalized Poisson sigma models that we define are related to the quantization deformation problems of coisotropic submanifolds using homotopical algebras.
