Operator algebras and statistical mechanics

  • Huzihiro Araki
Main Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 80)


Some topics in quantum statistical mechanics related to theory of operator algebras are reviewed.


Gauge Group Operator Algebra Time Translation Quantum Statistical Mechanic Boolean Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Ruelle: Cargése lectures in Physics (ed. D. Kastler, Gordon and Breach, New York, 1970) pp.169–194.Google Scholar
  2. [2]
    E. Størmer: loc. Cit. pp.195–213.Google Scholar
  3. [3]
    S. Doplicher and D. Kastler: Comm. Math. Phys. 7 (1968), 1–20.CrossRefGoogle Scholar
  4. [4]
    S. Sakai: Amer. J. Math. 98 (1976), 427–440.Google Scholar
  5. [5]
    R. F. Streater: Comm. Math. Phys. 6 (1968), 233–247.Google Scholar
  6. [6]
    D. W. Robinson: Comm. Math. Phys. 7 (1968), 337–348.Google Scholar
  7. [7]
    D. Ruelle: Statistical Mechanics (Benjamin, New York, 1969).Google Scholar
  8. [8]
    A. Kishimoto: Comm. Math. Phys. 47 (1976), 25–32.Google Scholar
  9. [9]
    R.T. Powers and S. Sakai: Comm. Math. Phys. 39 (1975), 273–288.Google Scholar
  10. [10]
    D. W. Robinson: Comm. Math. Phys. 16 (1970), 290–309.Google Scholar
  11. [11]
    S. Miracle-Sole and D. W. Robinson: Comm. Math. Phys. 19 (1970), 204–218.Google Scholar
  12. [12]
    J. Ginibre: Statistical Mechanics and Field Theory (ed. C. DeWitt and R. Stora, Gordon and Breach, New York, 1971) pp.327–427.Google Scholar
  13. [13]
    Y. M. Suhov: Limit Gibbs state for a class of one-dimensional systems of quantum statistical mechanics, preprint'Google Scholar
  14. [14]
    O. E. Lanford: Proceedings of the International Congress of Mathematicians ed. R. D. James, Canadian Math. Congress, 1975 vol.2, pp.377–381.Google Scholar
  15. [15]
    A. Kishimoto: Equilibrium states of a semi-quantum lattice system, to appear in Rep. Math. Phys.Google Scholar
  16. [16]
    H. Araki: Proceedings of the Second U.S.-Japan Seminar on C*-algebras and Applications to Physics, to be published.Google Scholar
  17. [17]
    M. Fannes and A. Verbeure: Correlation inequalities and equilibrium states. To appear in Comm. Math. Phys.Google Scholar
  18. [18]
    G. L. Sewell: KMS conditions and local thermodynamical stability of quantum lattice system II, to appear in Comm. Math. Phys.Google Scholar
  19. [19]
    H. Araki: C*-Algebras and Their Applications to Statistical Mechanics and Quantum Field Theory. (ed. D. Kastler, North Holand, 1976) pp. 64–100.Google Scholar
  20. [20]
    R. Haag, D. Kastler and E. B. Trych-Pohlmeyer: Comm. Math. Phys. 38 (1974), 173–193.Google Scholar
  21. [21]
    D. Kastler and O. Bratteli: Comm. Math. Phys. 46 (1976), 37–42.Google Scholar
  22. [22]
    H. Araki and A. Kishimoto: Comm. Math. Phys. 52 (1977), 211–232.Google Scholar
  23. [23]
    H. Araki, D. Kastler, M. Takesaki and R. Haag: Comm. Math. Phys. 53 (1977), 97–134.Google Scholar
  24. [24]
    A. Kishimoto: On invariant states and the commutant of a group of quasitfree automorphisms of the CAR algebra.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Huzihiro Araki
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

Personalised recommendations