Thermal momentum distribution from path integrals with shifted boundary conditions

Details Thermal momentum distribution from path integrals with shifted boundary conditions Thermal momentum distribution from path integrals with shifted boundary conditions

2010-11-11

arxiv.org/abs/1011.2727v2

Phys.Rev.Lett.106:131601,2011

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, 1 figure, minor revisions; version accepted in PRL

Scientific paper

10.1103/PhysRevLett.106.131601

For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction, and (b) the ordinary partition function. In this form the generating function is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.

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