Path Integrals pp 419-454 | Cite as

The Interacting Bose Fluid: Path Integral Representations and Renormalization Group Approach

  • F. W. Wiegel
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 34)


We review the various rigorous representations of the boson partition function as an integral over function space. Two approximation schemes for the evaluation of such path integrals are discussed: the saddle point method and the method of the renorma-lization group. These methods are applied to the critical behavior of the interacting Bose fluid. The saddle point method leads naturally to a description of the À transition in terms of quantized vortex lines which create microturbulence in the superfluid. The renormalization group approach leads to the conclusion that the critical behavior of the Bose fluid is identical to that of a classical system of spins with two components.


Partition Function Vortex Ring Path Integral Vortex Line Decomposition Property 


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  1. 1).
    F.W. Wiegel, Phys. Rep. 16 (1975) 57.MathSciNetADSCrossRefGoogle Scholar
  2. 2).
    S. P. Ohanessian, “The interacting Bose gas: formalism in coherent states and applications”, Thesis, Ecole Polytechnique Fédérale de Lausanne (1976).Google Scholar
  3. 3).
    F.W. Wiegel and J. Hijmans, Proc. Kon. Ned. Acad..B77 (1974) 177.MathSciNetGoogle Scholar
  4. 4).
    F.W. Wiegel and J. Hijmans, Proc. Kon. Ned. Acad. B77 (1974) 189.MathSciNetGoogle Scholar
  5. 5).
    R. Hirota, Thesis, Northwestern University (1961).Google Scholar
  6. 6).
    F.W. Wiegel and J.B. Jalickee, Physica 57 (1972) 317.MathSciNetADSCrossRefGoogle Scholar
  7. 7).
    F.W. Wiegel, Physica 65 (1973) 321.ADSCrossRefGoogle Scholar
  8. 8).
    G. Toulouse and P. Pfeuty: “Introduction au groupe de renormalisation et a ses applications”, Presses Univ. de Grenoble (1975).Google Scholar
  9. 9).
    S.K. Ma: “Moderne theory of critical phenomena”, Benjamin (1976).Google Scholar
  10. 10).
    C. Domb and M.S. Green: “Phase transitions and critical phenomena”, Vol. 6, Academic Press (1976).Google Scholar
  11. 11).
    K.K. Singh, Phys. Lett. 51A (1975) 27.ADSCrossRefGoogle Scholar
  12. 12).
    K.K. Singh, Phys. Lett. 57A (1976) 309.ADSCrossRefGoogle Scholar
  13. 13).
    M. Baldo, E. Catara and U. Lombardo, Lett. Nuov. Cim. 15 (1976) 214.CrossRefGoogle Scholar
  14. 14).
    S.P. Ohanessian and A. Quattropani, Helv. Phys. Acta 46 (1973) 473.Google Scholar
  15. 15).
    S.K. Ma, Phys. Rev. Lett. 29 (1972) 1311.ADSCrossRefGoogle Scholar
  16. 16).
    F. Family and H.E. Stanley, Phys. Lett. 53A (1975) 111.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • F. W. Wiegel
    • 1
  1. 1.Department of Applied PhysicsTwente University of TechnologyEnschedeThe Netherlands

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