Generating function, path integral representation, and equivalence for stochastic exclusive particle systems

TL;DR

This paper develops a path integral framework for classical exclusive particle systems, enabling the transformation of master equations into path integrals and demonstrating equivalences between different reaction-diffusion processes.

Contribution

It introduces a novel path integral representation for generating functions in exclusive particle systems using hard-core bosonic operators.

Findings

Path integral representation for generating functions derived.

Equivalence between single-species and two-species reaction-diffusion processes established.

Master equations transformed into linear path integral equations.

Abstract

We present the path integral representation of the generating function for classical exclusive particle systems. By introducing hard-core bosonic creation and annihilation operators and appropriate commutation relations, we construct the Fock space structure. Using the state vector, the generating function is defined and the master equation of the system is transformed into the equation for the generating function. Finally, the solution of the linear equation for the generating function is derived in the form of the path integral. Applying the formalism, the equivalence of reaction-diffusion processes of single species and two species are described.