Il Nuovo Cimento (1955-1965)

, Volume 11, Issue 5, pp 635–643 | Cite as

The partition function and the subsidiary conditions in the Bohm-Pines and Migdal-Galitsky’s supplementary variables method

  • A. Pawlikowski
  • W. Szczurówna


The supplementary variables method is applied to the approximate calculation of the partition function ofN interacting fermions. It is shown that the supplementary variables method in its original formulation due to Bohm-Pines and Migdal-Galitsky leads to wrong results. One obtains correct results if one assumes a modification, due to Kanazawa, of the subsidiary conditions in this method.


Il metodo delle variabili supplementari si applica al calcolo approssimato della funzione di ripartizione diN fermioni interagenti. Si dimostra che il metodo delle variabili supplementari nella sua formulazione originale dovuta a Bohm-Pines e a Migdal-Galitsky conduce a risultati errati. Si ottengono risultati corretti se si introduce una modificazione delle condizioni sussidiarie del metodo dovuta a Kanazawa.


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  1. (*).
    ·ome of results obtained here were published as a short note inDokl. Akad. Nauk SSSR,118, 61 (1958).Google Scholar
  2. (1).
    D. Pines:Solid state physics,1, 368 (1955).Google Scholar
  3. (2).
    D. N. Zubarev:Candidate’s degree dissertation (Moskow, 1953).Google Scholar
  4. (3).
    H. Kanazawa:Progr. Theor. Phys.,18, 287 (1957).MathSciNetADSCrossRefGoogle Scholar
  5. (4).
    S. N. Gupta:Proc. Phys. Soc., A63, 681 (1950);K. Bleuler:Helv. Phys. Acta,23, 567 (1950).ADSCrossRefGoogle Scholar
  6. (5).
    E. C. Titchmarsh:Introduction to the Theory of Fourier Integrals (Oxford, 1948), p. 77, theorem 53.Google Scholar
  7. (6).
    D. N. Zubarev:Dokl. Akad. Nauk SSSR,95, 757 (1954).MathSciNetMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1959

Authors and Affiliations

  • A. Pawlikowski
    • 1
  • W. Szczurówna
    • 1
  1. 1.Polska Akademia Nauk, Instytut FizykiPracownia StatystycznaWrocław

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