A Short Proof of the Reducibility of Hard-Particle Cluster Integrals

TL;DR

This paper proves that Mayer cluster integrals for n-dimensional hard particles can be simplified into basic components, making the partition function easier to compute using algebraic rules similar to Feynman diagrams.

Contribution

It provides a new proof demonstrating the complete reducibility of hard-particle cluster integrals into simpler measures, extending previous results to higher dimensions.

Findings

Graphs are reducible into 1- and 2-point measures

Partition function becomes perturbatively solvable

Algebraic rules akin to Feynman diagrams are established

Abstract

The current article considers Mayer cluster integrals of n-dimensional hard particles in the n>1 dimensional flat Euclidean space. Extending results from Wertheim and Rosenfeld, we proof that the graphs are completely reducible into 1- and 2-point measures, with algebraic rules similar to Feynman diagrams in quantum field theory. The hard-particle partition function reduces then to a perturbative solvable problem.