Geometry of Supersymmetry

  • Arthur Jaffe
  • Andrzej Lesniewski
Part of the NATO ASI Series book series (NSSB, volume 234)


These lectures are divided into three parts. The latter two chapters are mathematical, in the sense that all definitions are precise and results are formulated as theorems. The present chapter plays a different role. It provides a mixture of motivation and formal calculation. Some of the materials is or can be made mathematical; the presentation, however, is distinctly that from physics. A mathematician may wish to read this chapter for an overview; he will be more familiar with the style of Chapters II and III.


Cohomology Class Fredholm Operator Loop Space Chern Character Homotopy Invariance 
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.


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  1. [Cl]
    Connes, A.: Noncommutative Differential Geometry, Publ. Math. IHES 62 (1985), 257–360.MathSciNetGoogle Scholar
  2. [C2]
    Connes, A.: Entire Cyclic Cohomology of Banach Algebras and Characters of 8Summable Fredholm Modules, K-Theory, 1 (1988), 519–548.MathSciNetMATHCrossRefGoogle Scholar
  3. [EFJL]
    Ernst, K., Feng, P., Jaffe, A., and Lesniewski, A.: Quantum K-Theory II. Homotopy Invariance of the Chern Character, Jour. Funct. Anal., to appear.Google Scholar
  4. [GS]
    Getzler, E. and Szenes, A.: On the Chern character of theta-summable Fredholm modules, J. Funct. Anal.,to appear.Google Scholar
  5. [GJ]
    Glimm, J. and Jaffe, A.: Quantum Physics, Second Edition, Springer: New York 1987.CrossRefGoogle Scholar
  6. [H]
    Hamilton, R.: The Inverse Function Theorem of Nash and Moser, Bull. Amer. Math. Soc. 7 (1982), 65–222.MathSciNetMATHCrossRefGoogle Scholar
  7. [JL1]
    Jaffe, A. and Lesniewski, A.: A priori estimates for N=2 Wess-Zumino models on a cylinder, Commun. Math. Phys. 114 (1988), 553–575.MathSciNetADSMATHCrossRefGoogle Scholar
  8. [JL2]
    Jaffe, A. and Lesniewski, A.: Supersymmetric Field Theory and Infinite Dimensional Analysis, in Nonperturbative Quantum Field Theory, G. Hooft et al., Editors, Plenum, New York, 1988.Google Scholar
  9. [JL3]
    Jaffe, A. and Lesniewski, A.: An Index Theorem for Superderivations, Commun. Math. Phys., to appear.Google Scholar
  10. [JLL]
    Jaffe, A., Lesniewski, A., and Lewenstein, M.: Ground State Structure in Supersymmetric Quantum Mechanics, Ann. Phys. 178 (1987), 313–329.MathSciNetADSMATHCrossRefGoogle Scholar
  11. [JLO1]
    Jaffe, A., Lesniewski, A., and Osterwalder, K.: Quantum K-Theory I: The Chern Character, Commun. Math. Phys. 118 (1988), 1–14.MathSciNetADSMATHCrossRefGoogle Scholar
  12. [JLO2]
    Jaffe, A., Lesniewski, A., and Osterwalder, K.: On Super-KMS Functionals and Entire Cyclic Cohomology, K-Theory, to appear.Google Scholar
  13. [JLW1]
    Jaffe, A., Lesniewski, A., and Weitsman, J., Index of a Family of Dirac Operators on Loop Space, Commun. Math. Phys. 112, 75–88 (1987).MathSciNetADSMATHCrossRefGoogle Scholar
  14. [JLW2]
    Jaffe, A., Lesniewski, A., and Weitsman, J.: The Two-Dimensional, N=2 Wess-Zumino Model On a Cylinder. Commun. Math. Phys. 114 (1988), 147–165.MathSciNetADSMATHCrossRefGoogle Scholar
  15. [JLW3]
    Jaffe, A., Lesniewski, A., and Weitsman, J.: Pfaffians on Hilbert Space, J. Funct. Anal., 83 (1989), 348–363.MathSciNetMATHCrossRefGoogle Scholar
  16. [JLW4]
    Jaffe, A., Lesniewski, A., and Weitsman, J.: The Loop Space S1 → R and Supersymmetric Quantum Fields, Annals of Physics, 183 (1988), 337–351.MathSciNetADSMATHCrossRefGoogle Scholar
  17. [JLW5]
    Jaffe, A., Lesniewski, A., and Wieczerkowski, C.: A Priori Quantum Field Equations, Ann. Phys., to appear.Google Scholar
  18. [JLW6]
    Jaffe, A., Lesniewski, A., and Wisniowski, M.: Deformation of Super-KMS Function-als, Commun. Math. Phys., 121 (1989), 527–540.MathSciNetADSMATHCrossRefGoogle Scholar
  19. [K1]
    Karoubi, M.: K-Theory, Springer: New York 1978.MATHCrossRefGoogle Scholar
  20. [K2]
    Kastler, D.: Cyclic Cocycles from Graded KMS Functionals, Commun. Math. Phys., 121 (1989), 345–350.MathSciNetADSCrossRefGoogle Scholar
  21. [M]
    Manin, Yu.: Complex Geometry and Gauge Fields, Springer: 1988.Google Scholar
  22. [We]
    Weitsman, J.: A Supersymmetric Field Theory in Infinite Volume, PhD Thesis, Harvard University 1988.Google Scholar
  23. [WI]
    Witten, E.: Constraints on Supersymmetry Breaking, Nucl. Phys. B202 (1982), 253–316.MathSciNetADSCrossRefGoogle Scholar
  24. [W2]
    Witten, E.: Supersymmetry and Morse Theory, J. Diff. Geom. 17 (1982), 661–692.MathSciNetMATHGoogle Scholar
  25. [W3]
    Witten. E.: Global Anomalies in String Theory, in Anomalies, Geometry and Topology, 61–99, W. Bardeen and A. White, Eds., World Scientific, Singapore (1985).Google Scholar
  26. [W4]
    Witten, E.: Elliptic Genera and Quantum Field Theory, Commun. Math. Phys. 109 (1987), 525–536.MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Arthur Jaffe
    • 1
  • Andrzej Lesniewski
    • 1
  1. 1.Harvard UniversityCambridgeUSA

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