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

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.