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Non-Commutative Geometry and Mathematical Physics

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New Symmetry Principles in Quantum Field Theory

Part of the book series: NATO ASI Series ((NSSB,volume 295))

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Abstract

What is the role of mathematicsin physics?

We have come to accept, over the past few years, that physics can play a basic conceptual role in stimulating new points of view in mathematics. This can range, on the one hand, from giving technical insights into the proof of a theorem, to motivating, on the other hand, whole new subfields of investigation.

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References

  1. F. Berezin, General concepts of quantization, Commun. Math. Phys., 40 (1975) 153–174.

    Article  MathSciNet  ADS  Google Scholar 

  2. A. Connes, Non-commutative differential geometry, Publ. Math. IHES, 62 (1986), 257–360.

    Google Scholar 

  3. A. Connes, Entire cyclic cohomology of Banach algebras and characters of Θ-summable Fredholm modules, K-Theory, 1 (1988), 519–548.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Connes, On the Chern character of Θ-summable Fredholm modules, Commun. Math. Phys., 139 (1991), 171–181.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. A. Connes, Lectures at MIT, April 1991.

    Google Scholar 

  6. A. Connes and J. Lott, Non-commutative geometry and particle physics, Nuclear Physics B, 1990, and these proceedings.

    Google Scholar 

  7. R. Douglas, S. Hurder, and J. Kaminker, Cyclic cocycles, renormalization and eta-invariants, Invent. math., 103 (1991), 101–179.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. J.-P. Eckmann, Remarks on the classical limit of quantum field theories, Lett. Math. Phys., 1 (1977), 387–394.

    Article  MathSciNet  ADS  Google Scholar 

  9. K. Ernst, P. Feng, A. Jaffe, and A. Lesniewski, Quantum K-Theory, II. Homotopy invariance of the Chern character, Jour. Funct. Anal., 90 (1990), 355–368.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Glimm and A. Jaffe, The λ(ø4)2 quantum field without cutoffs III: the physical vacuum, Acta Math., 125 (1970), 203–267.

    Article  MathSciNet  Google Scholar 

  11. J. Glimm and A. Jaffe, “Quantum Physics,” Springer Verlag 1987.

    Book  Google Scholar 

  12. J. Glimm, A. Jaffe, and T. Spencer, The Wightman axioms and particle structure in the ρ(ø4)2 quantum field model, Ann. Math., 100 (1974), 585–632.

    Article  MathSciNet  Google Scholar 

  13. E. Getzler and A. Szenes, On the Chern character of a theta-summable module, J. Funct. Anal., 84 (1989), 343–357.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Jaffe and A. Lesniewski, Supersymmetric field theory and infinite dimensional analysis, in “Nonperturbative Quantum Field Theory,” Proceedings of the 1987 Cargèse Summer School, G. ‘t Hooft et. al., Editors, Plenum Press 1988.

    Google Scholar 

  15. A. Jaffe and A. Lesniewski, Geometry of supersymmetry, 1988 Erice Lectures, G. Velo and A. Wightman, Editors, by Plenum Press, New York, 1990.

    Google Scholar 

  16. A. Jaffe and A. Lesniewski, 1990–1991 Harvard University Lectures on “Quantum fields, geometry, and analysis in infinite dimensions,” to appear.

    Google Scholar 

  17. A. Jaffe, A. Lesniweski, and K. Osterwalder, Quantum K-Theory, I. The Chem character, Commun. Math. Phys., 118 (1989), 1–14.

    Article  ADS  Google Scholar 

  18. A. Jaffe, A. Lesniewski, and K. Osterwalder, On super-KMS functionals and entire cyclic cohomology, K-Theory, 2 (1989), 675–682.

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Jaffe, A. Lesniewski and M. Wisniowski, Deformations of super-KMS function-als, Commun. Math. Phys., 121 (1989), 527–540.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. A. Jaffe and K. Osterwalder, Ward identities for non-commutative geometry, Commun. Math. Phys., 132 (1990), 119–130.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. S. Janowsky and J. Weitsman, A vanishing theorem for supersymmetric quantum field theory and finite size effects in multi-phase cluster expansions, Commun. Math. Phys., to appear.

    Google Scholar 

  22. D. Kastler, Cyclic cocycles from graded KMS functionals, Commun. Math. Phys., 121 (1989), 345–350.

    Article  ADS  Google Scholar 

  23. S. Klimek and A. Lesniewski, Quantum Riemann surfaces, Commun. Math. Phys., to appear.

    Google Scholar 

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© 1992 Springer Science+Business Media New York

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Jaffe, A. (1992). Non-Commutative Geometry and Mathematical Physics. In: Fröhlich, J., ’t Hooft, G., Jaffe, A., Mack, G., Mitter, P.K., Stora, R. (eds) New Symmetry Principles in Quantum Field Theory. NATO ASI Series, vol 295. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3472-3_10

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  • DOI: https://doi.org/10.1007/978-1-4615-3472-3_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6538-9

  • Online ISBN: 978-1-4615-3472-3

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