BRST and Topological Gauge Theories

Doctoral thesis, 2002

In this thesis, the BRST-quantization of gauge theories is discussed. A detailed analysis of the BRST-quantization on inner product spaces is performed for a class of abelian models, including reparametrization invariant ones. General rules how to obtain physical wave functions and propagators are proposed. The gauge fixing fermion is seen to play a central role for an admissible choice of the specific state space representation. Canonically equivalent solutions to the quantum master equation is found for a class of first order field theories, using a superfield formulation of the BV-framework. The analysis performed in d = 4 and d = 6 dimensions, shows that many master actions actually are canonically equivalent to simpler (minimal) master actions. The geometrical framework of almost product structures (APS) is adopted in order to investigate the splitting of manifolds induced by for example Yang-Mills theories and Kaluza-Klein theories. The properties of the Riemann-tensor are analyzed via the APS ansatz. New curvature relations are found in terms of the so called Vidal- and adapted connections.