A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field.

Abstract:

Since their introduction in the early 40s Feynman path integrals have represented, on the one hand, a powerful technique and, on the other hand, a mathematical challenge. Several approaches for their rigorous mathematical definition have been proposed, but a final and complete theory is still lacking and several - seemingly simple -  problems are still open. In this talk I shall present a particular toy model showing how techniques of stochastic analysis can be effectively  applied in this context and pointing out possible developments.