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arXiv · 1907.11928

A rigorous mathematical construction of Feynman path integrals for the Schr\"odinger equation with magnetic field

Sergio Albeverio·Nicolò Cangiotti·Sonia Mazzucchi
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Abstract

A Feynman path integral formula for the Schr\"odinger equation with magnetic field is rigorously mathematically realized in terms of infinite dimensional oscillatory integrals. We show (by the example of a linear vector potential) that the requirement of the independence of the integral on the approximation procedure forces the introduction of a counterterm to be added to the classical action functional. This provides a natural explanation for the appearance of a Stratonovich integral in the path integral formula for both the Schr\"odinger and heat equation with magnetic field.

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Sergio Albeverio, Nicolò Cangiotti, Sonia Mazzucchi. 2019-07-27. A rigorous mathematical construction of Feynman path integrals for the Schr\"odinger equation with magnetic field. https://arxiv.org/abs/1907.11928

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