Advertisement

Cyclic Cohomology, Supersymmetry and KMS States the KMS States as Generalized Elliptic Operators

  • Daniel Kastler
Part of the NATO ASI Series book series (NSSB, volume 245)

Abstract

Let me begin this talk at a conference devoted to the interface between physics and geometry by stressing the essential identity of geometry and analysis. The distinction is one of methods. The common theme is manifolds and the pseudodifferential operators attached to their vector bundles.

Keywords

Vector Bundle Dirac Operator Elliptic Operator Loop Space Chern Character 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1].
    A. Connes, Pub. Math. IHES 62 257 (1985)MathSciNetGoogle Scholar
  2. [2].
    A. Connes, K-Theory 1 519 (1988)MathSciNetMATHCrossRefGoogle Scholar
  3. [2a].
    A. Connes, Pacific. J. Math. 137 225 (1989)MathSciNetMATHCrossRefGoogle Scholar
  4. [3].
    D. Kastler, CMP 121 345 (1989)MathSciNetGoogle Scholar
  5. [4].
    A. Jaffe, A. Lesniewski, K. Osterwalder CMP 118 1 (1988)MathSciNetMATHGoogle Scholar
  6. [5].
    A. Connes, Ann. Sc. Ec. Norm. Sup. 6 133 (1973)MathSciNetMATHGoogle Scholar
  7. [6].
    A. Connes, Ann. Math. 104 73 (1976)MathSciNetMATHCrossRefGoogle Scholar
  8. [7].
    A. Connes, Proc. Symp. Pur. Math. 38 43 (1982)MathSciNetCrossRefGoogle Scholar
  9. [8].
    U. Haagerup, Acta Math. 104 73 (1976)Google Scholar
  10. [9].
    H. Araki, J. Math. Phys. 4 1343 (1963)MathSciNetADSMATHCrossRefGoogle Scholar
  11. [10].
    N. Hugenholtz, CMP, 6 189 (1967)MathSciNetMATHGoogle Scholar
  12. [11].
    W. Driessler, CMP. 44 133 (1975)MathSciNetMATHGoogle Scholar
  13. [12].
    R. Longo, Proc. Symp. Pur. Math. 38 551 (1982)MathSciNetCrossRefGoogle Scholar
  14. [13].
    M. Tomita, Vth Funct. Anal. Symp. Math. Soc. Japan Sendai (1967)Google Scholar
  15. [14].
    M. Takesaki, Springer Lecture Notes Math. 128 (1970)Google Scholar
  16. [15].
    R. Haag, N. Hugenholtz; M. Winnink CMP 5 215 (1967)MathSciNetMATHGoogle Scholar
  17. [16].
    M. Takesaki, Acta Math. 131 249 (1973)MathSciNetMATHCrossRefGoogle Scholar
  18. [17].
    D. Kastler, Symposia Math. XX 49 (1976)MathSciNetGoogle Scholar
  19. [17a].
    D. Kastler, Proc. Symp. Pur. Math. 38 467 (1982)MathSciNetCrossRefGoogle Scholar
  20. [18].
    R. Haag, D. Kastler, E.B. Trych-Pohlmeyer, CMP 38 173 (1974)MathSciNetGoogle Scholar
  21. [19].
    W. Push, S. Woronowiz, CMP 58 273 (1978)Google Scholar
  22. [20].
    H. Araki, R. Haag, D. Kastler, M. Takesaki, CMP 53 97 (1977)MathSciNetGoogle Scholar
  23. [21].
    O. Bratteli, D. Robinson. Vol. II, texts and monographies in Physics Springer (1981)Google Scholar
  24. [22].
    K. Fredenhagen, K.H. Rehren, B. Schroer, Inst. Theor. Elementarteilchen Preprint Berlin (1988)Google Scholar
  25. [23].
    M. Atiyah K-theory Benjamin (1907)Google Scholar
  26. [24].
    B. Blackadar, K-theory for operator algebras, Springer MSRI series, Springer 1986.CrossRefGoogle Scholar
  27. [25].
    M. Atiyah, Proc. Int. Conf. Funct. Anal. Tokyo Univ. Press (1970) Mat. 44 57 (1980)Google Scholar
  28. [26].
    G. Kasparov. Izv. Akad. Nauk. SSSR Ser. Mat. 44 57 (1980)MathSciNetGoogle Scholar
  29. [27].
    D. Kastler, Travaux en cours 30, Ed. Hermann, Paris (1988)Google Scholar
  30. [28].
    D. Kastler, CPT Preprint 88/P. 21–28 Marseille (1988)Google Scholar
  31. [29].
    J. Cuntz, K-Theory 1 31 (1987)MathSciNetMATHCrossRefGoogle Scholar
  32. [30].
    A. Connes, Private communicationGoogle Scholar
  33. [31].
    A. Jaffe, A. Lesniewski, A. Weitsman CMP 112 75 (1987)MathSciNetMATHGoogle Scholar
  34. [32].
    D. Kastler, K-theory 1 485 (1989)MathSciNetCrossRefGoogle Scholar
  35. [33].
    A. Jaffe, A. Lesniewski, K. Osterwalder, Preprint HUTMP, 88/B-229 HarvardGoogle Scholar
  36. [34].
    A. Jaffe, A. Lesniewski, M. Wisniowski HUTMP 88/B-231, Harvard.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Daniel Kastler
    • 1
  1. 1.Centre de Physique ThéoriqueCNRS — Luminy — Case 907Marseille Cedex 9France

Personalised recommendations