Skip to main content
SpringerLink
Log in
Book cover

Mathematical Results in Quantum Mechanics pp 219–226Cite as

Birkhäuser

Poisson Field Representations in the Statistical Mechanics of Continuous Systems

  • Chapter

  • 326 Accesses

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 70))

Abstract

The grand canonical Gibbs ensembles describing continuous systems of particles are represented as functional integrals with respect to some infinitely divisible generalized random fields. Several applications like the convergence of cluster expansions for a wide class of interactions and the existence of the limiting Gibbs measures are presented.

Research supported by the Polish National Committee of Science

†

Research supported by Ukrainian State Committee of Science and Technology

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Federbush P. Kennedy T., Surface effects in Debye screening, Comm. Math. Phys. 43, 55–97 (1988).

    MathSciNet  Google Scholar 

  2. Rebenko A.L., Mathematical Foundations of Equilibrium Classical Statistical Mechanics of charged particles, Russ.Math.Surv. 43, 55–97 (1980) and refs. therein.

    MathSciNet  Google Scholar 

  3. Ruelle D., Statistical mechanics: Rigorous results, New York, Amsterdam: Benjamin 1969.

    MATH  Google Scholar 

  4. Petrina D.Ya., Gerasimenko V.J. Malyshew P.V. Mathematical Foundation of Classical Statistical Mechanics. Continous System., New York, London, Paris, Gordon and Breach Science, 1989.

    Google Scholar 

  5. Gielerak, R., Rebenko, A.L., Poisson Integral representation in the Statistical Mechanics of Continuous Systems, paper in preparation.

    Google Scholar 

  6. Ph. Combe, R. Hoegh-Krohn, R. Rodriguez, M. Siruge, M. Siruge-Collin, Comm. Math. Phys. 77, 269-288.

    Google Scholar 

  7. Albeverio S., Iwata K., Hoegh-Krohn R., Random fields as solutions of the inhomogenous quaternionic Cauchy-Riemann equations, Poisson Processes on Groups and Feynman path Integrals, Comm.Math.Phys. 132, 555–580 (1981).

    Article  ADS  Google Scholar 

  8. Klauder, J.R., Measures and support in functional integration, pp. 31-56 in “Progress in Quantum Field Theory”, Eds: H. Ezawa, S. Kamefuchi, Elsevier Science 1986, and refs, therein.

    Google Scholar 

  9. Gelfand J.M., Vilenkin N.Ya, Generalized functions Vol.4. Applications of harmonic analysis. New York, London: Academic Press 1968.

    Google Scholar 

  10. Rebenko A.L., Poisson Measure representation and Cluster Expansion in Classical Statistical Mechanics, Comm.Math.Phys. 151, 427–435 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Brydges D., Fedurbusti P., The cluster expansion in statistical mechanics, Comm.Math.Phys. 49, 233–246 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  12. Ruelle D., Superstable Interactions in Classical Statistical mechanics, Comm. Math. Phys. 18, 127 (1970).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Ginibre J., Reduced Density Matrices of Quantum Gases, I,II,III: Journ. Math. Phys. 6(2) 238–251 (1965), 6(2), 252-262 (1965), 6 1432-1446 (1965).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Ginibre J., Phase Transitions and Critical Phenomena, vol 1, Domb I.C. and Green M.S. eds pp 11–136, Academic Press, New York 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wroclaw, 50-205, Wroclaw, Poland

    Roman Gielerak

  2. Institute of Mathematics, Acad. Sci. Ukraine, Repin Street, 252601, Kiev, Ukraine

    Alexei L. Rebenko

Authors
  1. Roman Gielerak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexei L. Rebenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technische Universität Clausthal, Institut für Mathematik, Erzstrasse 1, D-38678, Clausthal-Zellerfeld, Germany

    M. Demuth

  2. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Head Post Office Box 79, Moscow, Russia

    P. Exner

  3. Fachbereich Mathematik MA 7-2, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623, Berlin, Germany

    H. Neidhardt

  4. Université d’Aix-Marseille II et, Centre de Physique Théorique, CNRS — Luminy — Case 907, F-13288, Marseille Cedex 9, France

    V. Zagrebnov

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Basel AG

About this chapter

Cite this chapter

Gielerak, R., Rebenko, A.L. (1994). Poisson Field Representations in the Statistical Mechanics of Continuous Systems. In: Demuth, M., Exner, P., Neidhardt, H., Zagrebnov, V. (eds) Mathematical Results in Quantum Mechanics. Operator Theory: Advances and Applications, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8545-4_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8545-4_27

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9673-3

  • Online ISBN: 978-3-0348-8545-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation