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Path integration method in the theory of model Hamiltonians

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Abstract

The path integtation method is used to obtain the asymptotic behavior of the ratio Z/Z0 for a model of the BCS type (Z is the statistical sum of the model, Z0 is the statistical sum of the free system) in the limit V → ∞. The asymptotic formulas for Z/Z0 are different above and below the transition and are expressed in terms of infinite products. A rigorous proof is obtained for the formulas under the condition of fulfillment of a natural additional assumption.

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Literature cited

  1. N. N. Bogolyubov, Jr., A Method for Studying Model Hamiltonians, Pergamon Press, Oxford (1972).

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  2. B. V. Moshchinskii, Dissertation, Dubna (1978).

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Authors
  1. V. N. Popov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 101, pp. 128–150, 1981.

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Popov, V.N. Path integration method in the theory of model Hamiltonians. J Math Sci 23, 2453–2465 (1983). https://doi.org/10.1007/BF01084174

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  • DOI: https://doi.org/10.1007/BF01084174

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