Gaussian Reformulation of the Feynman Path Integral for Quantum Statistical Mechanics with Results for the Second Virial Coefficient of $^4$He

Phil Attard

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arXiv · 2607.16301

Gaussian Reformulation of the Feynman Path Integral for Quantum Statistical Mechanics with Results for the Second Virial Coefficient of $^4$He

Phil Attard

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Abstract

The Feynman path integral for quantum statistical mechanics is reformulated as Gaussian sampling of the neighborhood of each position configuration. The variance and mean are obtained from ring polymer statistics on a lattice, and from the high temperature expansion of the Wigner-Kirkwood commutation function, respectively. The algorithm avoids multiple temperature nodes for each configuration and the need for numerical cancelation in the statistical averages, which are problematic for conventional path integral quantum Monte Carlo. Analytic and simulation results for the second virial coefficient of helium are compared to laboratory measurements.

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Phil Attard. 2026-07-14. Gaussian Reformulation of the Feynman Path Integral for Quantum Statistical Mechanics with Results for the Second Virial Coefficient of $^4$He. https://arxiv.org/abs/2607.16301

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