A partition function representation through Grassmann variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 2, pp. 301-310
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We propose a formula for a classical partition function $Z_N$ that does not involve the Hamilton function of the system. In the general case, we avoid passing to canonical variables $(\mathbf p,\mathbf x)$ at the price of extending the space of Lagrange variables $(\mathbf v,\mathbf x)$ by introducing “additional velocities” $\bar{\mathbf u},\mathbf u$, which are the generators of a Grassmann algebra. In this space, the partition function $Z_N$ is the integral of a Gibbs-type distribution, whose explicit form is determined by the system Lagrange function. We calculate the partition function of a model system governed by the Darwin Lagrange function.
@article{TMF_2001_126_2_a10,
author = {L. F. Blazhievskii},
title = {A partition function representation through {Grassmann} variables},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {301--310},
publisher = {mathdoc},
volume = {126},
number = {2},
year = {2001},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2001_126_2_a10/}
}
L. F. Blazhievskii. A partition function representation through Grassmann variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 2, pp. 301-310. http://geodesic.mathdoc.fr/item/TMF_2001_126_2_a10/