Exact Results in Quantum Theory & Gravity

The goal of this work is a rigorous perturbative construction of the SU(2) Yang-Mills theory in four dimensional Euclidean space. The functional integration technique gives a mathematical basis for establishing the renormalization group equations. While introduction of a momentum space regulator removes the divergences of the Schwinger functions, the important difficulty of the approach is the fact that the regulator breaks the gauge invariance. Thus the main part of the work is to prove at all loop orders the existence of the vertex functions and the restoration of the Slavnov-Taylor identities in the limit of the vanishing regulator.

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