Berezin Integrals and Poisson Processes

TL;DR

This paper connects Berezin integrals over anticommuting variables to expectations of Poisson process functionals using a Feynman-Kac formula, enabling classical analysis tools to evaluate these integrals.

Contribution

It introduces a novel method to compute Berezin integrals by reducing them to Poisson process expectations, bridging quantum calculus and stochastic analysis.

Findings

Reduction of Berezin integrals to Poisson process expectations

Application of Feynman-Kac formula to anticommuting variables

Derivation of a simple upper bound for Berezin integrals

Abstract

We show that the calculation of Berezin integrals over anticommuting variables can be reduced to the evaluation of expectations of functionals of Poisson processes via an appropriate Feynman-Kac formula. In this way the tools of ordinary analysis can be applied to Berezin integrals and, as an example, we prove a simple upper bound. Possible applications of our results are briefly mentioned.