Rigorous Functional Integration with Applications in QFT

The purpose of this note is to illustrate through Nelson’s and the PauliFierz models how functional integration can be applied in a rigorous way to solve problems of quantum field theory. The mathematical approach has specific benefits. Although for technical reasons particular proofs may involve restrictions on the reach of statements, the conclusions are reliable against a clear background of hypotheses. Secondly, this approach does allow to derive genuinely new results or understanding. Finally, the concepts and tools of modern stochastic analysis have a far reaching potential of cross-fertilizing the methods developed by physicists. For the details and proofs of the summary presentation below we refer to the (severely selected) bibliography.