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Russian Physics Journal

Calculation of partition function by the method of coherent states

L. F. Novikov

Published Oct 1, 1976• 0 citations
Publisher
DOI
10.1007/bf00891197

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理论物理通讯：英文版•Jan 1, 2005•0 citations
We introduce a Grassmannian version of the Stratonovich-Hubbard transformation and derive a new functional-integral representation for the grand partition function F (β) of many-fermion N -particle systems. A new separable form for Z (β) is found using both a disentangling method for "the evolution operator" and the dynamical super-Weyl group SW ( N ). Employing fermionic coherent states the relevant trace is calculated exactly. The case of a separable potential is analyzed in some detail.
The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and ψ4 theory as examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and ψ4 theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.