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A partition function representation through Grassmann variables
L. F. Blazhievskii Ivan Franko National University of L'viv
Abstract:
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.
Received: 18.04.2000 Revised: 10.08.2000
Citation:
L. F. Blazhievskii, “A partition function representation through Grassmann variables”, TMF, 126:2 (2001), 301–310; Theoret. and Math. Phys., 126:2 (2001), 250–257
Linking options:
https://www.mathnet.ru/eng/tmf432https://doi.org/10.4213/tmf432 https://www.mathnet.ru/eng/tmf/v126/i2/p301
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