The Feynman-Kac formula in deformation quantization

TL;DR

This paper introduces a Feynman-Kac formula within deformation quantization, enabling computation of ground state energies through phase space integrals of star exponentials, offering a new approach for physical models.

Contribution

It develops a novel Feynman-Kac formula in deformation quantization, connecting phase space integrals with ground state energy calculations after Wick rotation.

Findings

Ground state energies can be obtained from phase space integrals of star exponentials.

The method provides an efficient way to compute energies for certain physical models.

Examples demonstrate the practical application of the formula.

Abstract

We introduce the Feynman-Kac formula within the deformation quantization program. Constructing on previous work it is shown that, upon a Wick rotation, the ground state energy of any prescribed physical system can be obtained from the asymptotic limit of the phase space integration of the star exponential of the Hamiltonian operator. Some examples of this correspondence are provided showing a novel and efficient way of computing the ground state energy for some physical models.