Gauge Theories in Local Causal Perturbation Theory

Abstract

In this thesis quantum gauge theories are considered in the framework of local, causal perturbation theory. Gauge invariance is described in terms of the BRS formalism. Local interacting field operators are constructed perturbatively and field equations are established. A nilpotent BRS transformation is defined on the local algebra of fields. It allows the definition of the algebra of local observables as an operator cohomology. This algebra of local observables can be represented in a Hilbert space. The interacting field operators are defined in terms of time ordered products of free field operators. For the results above to hold the time ordered products must satisfy certain normalization conditions. To formulate these conditions also for field operators that contain a spacetime derivative a suitable mathematical description of time ordered products is developed. Among the normalization conditions are Ward identities for the ghost current and the BRS current. The latter are generalizations of a normalization condition that is postulated by Dutsch, Hurth, Krahe and Scharf for Yang-Mills theory. It is not yet proven that this condition has a solution in every order. All other normalization conditions can be accomplished simultaneously. A principle for the correspondence between interacting quantum fields and interacting classical fields is established. Quantum electrodynamics and Yang-Mills theory are examined and the results are compared with the literature.