Feynman path integral for Schrödinger equation with magnetic field

Cycle 32th Oral Defence of the Phd Thesis

14 February 2020
Versione stampabile

Venue: Povo Zero, via Sommarive 14 (Povo) – Seminar Room “-1”
Time: 11.00 a.m.

  • Nicolò Cangiotti - PhD in Mathematics

Abstract

Feynman path integrals, introduced heuristically in the 1940s, are a powerful tool used in many areas of physics, but also an intriguing mathematical challenge.
In this work we provide a rigorous mathematical Feynman path integral formula in the context of infinite dimensional oscillatory integrals. Moreover, the requirement of independence of the integral on the approximation procedure forces the introduction of a counterterm, which has to be added to the classical action functional (this is done by the example of a linear vector potential). Thanks to that, it is possible to give a natural explanation for the appearance of the Stratonovich integral in the path integral formula for both the Schrödinger and the heat equation with magnetic field.

Supervisor: Sonia Mazzucchi