One-parameter extension of the Doi-Peliti formalism and relation with orthogonal polynomials

TL;DR

This paper introduces a one-parameter extension of the Doi-Peliti formalism for stochastic chemical kinetics, linking it to orthogonal polynomials like Charlier and Hermite, and deriving consistent path-integral expressions.

Contribution

It presents a novel extension of the Doi-Peliti formalism that connects to orthogonal polynomials, enabling explicit polynomial-based representations.

Findings

Path-integral expressions consistent with previous studies

Explicit connections to Charlier and Hermite polynomials

Enhanced formalism for stochastic chemical kinetics

Abstract

An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected to orthogonal polynomials. We show that two different orthogonal polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to express the Doi-Peliti formalism explicitly.