Rigorous Feynman path integrals, with applications to quantum theory, gauge fields, and topological invariants

Rigorous Feynman path integrals are introduced and their relations with probabilistic infinite dimensional integrals (like Wiener integrals) explained. The corresponding rigorous methods of stationary phase for the study of the asymptotics of such integrals axe described and put in relation with the corresponding Laplace methods for probabilistic integrals. Applications are given to quantum theory. In the second part special attention is given to applications to the theory of quantized gauge fields and their relations to topological invariants (knot invariants, low dimensional manifolds). The geometry of classical/quantized gauge fields is also given special attention. The rigorous construction and the computation of knot invariants from rigorous Feynman path integrals for the Chern-Simons model on R-3 is described in detail.