Il Nuovo Cimento (1955-1965)

, Volume 31, Issue 1, pp 140–163 | Cite as

Statistical mechanical evaluation of phase-space integrals

  • F. Lurçat
  • P. Mazur


A method, based on the formalism of statistical mechanics, is presented, yielding for phase-space integrals and related quantities an asymptotic expansion valid forN→∞. It appears that, by retaining only the first two terms of this expansion, one gets approximate expressions which give satisfactory estimates even at low multiplicities (for instance, atN=5 the relative error is ∼ 1%). In a self-contained section, the formulae for the practical evaluation of phase-space integrals, according to this method, are listed.


Si descrive un metodo, basato sul formalismo della meccanica statistica, che dà uno sviluppo asintotico degli integrali dello spazio delle fasi e delle grandezze correlate, perN→∞. Risulta che, prendendo solo i primi due termini di questo sviluppo, si ottengono espressioni approssimate che dànno stime soddisfacenti anche per basse molteplicità (per es., perN=5 l’errore relativo è di ∼ 1%). In una sezione autonoma, si elencano le formule per la valutazione degli integrali dello spazio delle fasi secondo questo metodo.


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  1. (1).
    R. Hagedorn:Fortschr. der Phys.,9, 1 (1961). See also:Proc. Intern. Conf. on Theoretical Aspects of Very-High-Energy Phenomena, Report CERN 61-22 (1961).ADSMathSciNetCrossRefGoogle Scholar
  2. (2).
    M. Kretzschmar:Ann. Rev. Nucl. Sci.,11, 1 (1961).ADSCrossRefGoogle Scholar
  3. (3).
    H. W. Lewis:Proc. Berkeley Statistical Symposium (1951).Google Scholar
  4. (4).
    P. P. Srivastava andG. Sudarshan:Phys. Rev.,110, 765 (1958).ADSCrossRefGoogle Scholar
  5. (5).
    B. P. Desai:Phys. Rev.,119, 1390 (1960).ADSCrossRefGoogle Scholar
  6. (6).
    G. I. Kopylov: Preprint Dubna P-777 (1961).Google Scholar
  7. (7).
    D. J. Jones: Report CERN 63-1 (1963).Google Scholar
  8. (8).
    M. Neuman:An. Acad. Bras. Cienc.,31, 361, 487 (1959).Google Scholar
  9. (9).
    G. E. A. Fialho:Phys. Rev.,105, 328 (1957).ADSCrossRefGoogle Scholar
  10. (*).
    The same remark seems to hold also for the work ofKolkunov (10) who recently applied a similar method to (1).Google Scholar
  11. (10).
    V. A. Kolkunov:Žurn. Ėksp. Teor. Fiz.,43, 1448 (1962).Google Scholar
  12. (11).
    T. Ericson:Nuovo Cimento,21, 605 (1961).MathSciNetCrossRefGoogle Scholar
  13. (12).
    A. I. Khinchin:Mathematical Foundations of Statistical Mechanics (New York, 1949).Google Scholar
  14. (13).
    A. Erdelyi, W. Magnus, F. Oberhettinger andF. Tricomi:Tables of Integral Transforms (New York, 1953).Google Scholar
  15. (14).
    P. Mazur andJ. van der Linden:Journ. Math. Phys.,4, 271 (1963).ADSCrossRefGoogle Scholar
  16. (*).
    See reference (12), and also the Appendix.Google Scholar
  17. (15).
    G. Flamand: unpublished (private communication). Also quoted in:R. Hagedorn:Nuovo Cimento,25, 1017 (1962).Google Scholar
  18. (16).
    G. Pinski:Nuovo Cimento,24, 719 (1962).CrossRefGoogle Scholar
  19. (17).
    G. N. Watson:Theory of Bessel Functions (Cambridge, 1944).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1964

Authors and Affiliations

  • F. Lurçat
    • 1
  • P. Mazur
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-Yvette (S.-et-O.)

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