Mathematical definition of Feynman path integrals

Luogo:  Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari "-1"
Ore 14:00

• Relatore: Sonia Mazzucchi (Università di Trento)

Abstract:
In 1942 R. Feynman proposed an heuristic functional integral representation for the solution of the Schrödinger equation, computing the wave function of a non-relativistic quantum particle as a "sum over all possible histories of the system''. Despite the lack of mathematical rigor, "Feynman path integrals'' are widely used in many areas of theoretical physics, not only as a computational tool, but also as a particularly effective quantization method.
From a mathematical point of view, their precise definition is rather difficult and requires the implementation of an integration theory on infinite dimensional spaces alternative to the Lebesgue "traditional" one, in order to handle the lack of absolute convergence of Feynman integrals.
In this talk I shall give an overview of of the main mathematical problems in the definition of Feynman path integrals as well as the possible solution. Some recent results
and applications will also be discussed.

Referente: Davide Pastorello