Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics

2023/07/06 by Drago, Nicoló, Mazzucchi, Sonia, Moretti, Valter
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.03282

Abstract

In this work we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The main tools we use are the Cartan development map, the notion of oscillatory integral, and the Chernoff approximation theorem. We prove that, for a class of functions of a dense subspace of the relevant Hilbert space, the Feynman map produces the solution of the Schrödinger equation, where the Laplace-Beltrami operator coincides with the second order Casimir operator of the group.

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