Gauge field optimization of classical fluid expansions

For fluid systems with pairwise particle interactions, the traditional Mayer diagrammatic series expansion of the grand potential in fugacity is generalized by introducing a gauge degree of freedom via local vertex factors. Finite series truncations are then used to determine variationally the effective gauge field. For a test model of hard-core particles in three dimensions, the accuracy of the results for the pressure, resulting from optimization of the first few truncation orders, is comparable with that of the best fitting formula proposed ad hoc by Carnahan, N. F., and Starling, K. E., 1969, J. chem. Phys., 51, 635.