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Statistics and Monodromy in Two- and Three-Dimensional Quantum · Field Theory

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Differential Geometrical Methods in Theoretical Physics

Part of the book series: NATO ASI Series ((ASIC,volume 250))

Abstract

In Section 1, we review results on the statistics of local fields in two-dimensional relativistic quantum field theory and on the monodromy properties of Euclidean Green functions in conformal field theory. In Section 2, we describe three-dimensional gauge theories with particles of arbitrary real spin and intermediate statistics of interest in two-dimensional condensed matter physics.

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References

  1. Jürg Fröhlich, “Statistics of Fields, the Yang-Baxter Equation, and the Theory of Knots and Links”, to appear in the proceedings of the Cargèse summer school on string theory, conformal field theory and renormalization theory, 1987

    Google Scholar 

  2. A.B. Zamolodehikov, as quoted in: “Spectrum and Scattering of Excitations in the One-Dimensional Isotropic Heisenberg Model”, by L.D. Faddeev and L.A. Takhtadzhyan

    Google Scholar 

  3. K. Osterwalder and R. Schrader, Commun.Math.Phys. 31, 83 (1973),

    Article  MathSciNet  MATH  Google Scholar 

  4. K. Osterwalder and R. Schrader, Commun.Math.Phys. 42, 281 (1975);

    Article  MathSciNet  MATH  Google Scholar 

  5. V. Glaser, Commun.Math.Phys. 37, 257 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  6. A.A. Belavin, A.M. Polyakov and A.B. Zamolodchkov, Nucl.Phys. B 241, 333 (1984)

    Article  MATH  Google Scholar 

  7. V.S. Dotsenko and V.A. Fateev, Nucl. Phys. B 240 [FS 12], 312 (1984),

    Article  MathSciNet  Google Scholar 

  8. V.S. Dotsenko and V.A. Fateev, Nucl. Phys. B 251 [FS 13], 691 (1985).

    Article  MathSciNet  Google Scholar 

  9. P. Christe and R. Flume, Nucl. Phys. B282, 466 (1987); P. Christe, Ph.D. thesis, Bonn 1986

    Article  MathSciNet  Google Scholar 

  10. V.G. Knizhnik and A.B. Zamolodchikov, Nucl. Phys. B 247, 83 (1984);

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Tsuchiya and Y. Kanie, Lett. Math. Phys. 13, 303 (1987);

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Kohno, “Linear Representations of Braid Groups and Classical Yang-Baxter Equations” in: “Contemporary Mathematics: Artin’s Braid Group”, Santa Cruz, 1987

    Google Scholar 

  13. K.H. Rehren and B. Schroer, “Quasiprimary Fields: An Approach to Positivity of 2D Conformal Quantum Field Theory”, Preprint 1987; K.H. Rehren, “Locality of Comformal Fields in Two Dimensions: Exchange Algebra on the Light-Cone”, Preprint 1987, to appear in Commun. Math. Phys.

    Google Scholar 

  14. A. Capelli, C. Ithykson and J.B. Zuber, Nucl. Phys. B 280, 445 (1987);

    Article  Google Scholar 

  15. A. Capelli, C. Ithykson and J.B. Zuber, Commun. Math. Phys. 113, 1 (1987)

    Article  Google Scholar 

  16. R. Haag and D. Kastler, J. Math. Phys. 5, 848 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Doplicher, R. Haag and J.E. Roberts, Commun. Math. Phys. 13, 1 (1969) ;

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Doplicher, R. Haag and J.E. Roberts, Commun. Math. Phys. 15, 173 (1969);

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Doplicher, R. Haag and J.E. Roberts, Commun. Math. Phys. 23, 199 (1971);

    Article  MathSciNet  Google Scholar 

  20. S. Doplicher, R. Haag and J.E. Roberts, Commun. Math. Phys. 35, 49 (1974)

    Article  MathSciNet  Google Scholar 

  21. D. Buchholz and K. Fredenhagen, Nucl. Phys. B 154, 226 (1979);

    Article  Google Scholar 

  22. D. Buchholz and K. Fredenhagen, Commun. Math. Phys. 84, 1 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  23. D. Buchholz and H. Epstein, Fisika, 17, 32943 (1986)

    Google Scholar 

  24. R.F. Streater and A.S. Wightman, “PCT, Spin and Statistics and All That”, Reading, Mass.: Benjamin 1978

    Google Scholar 

  25. R. Jost, “The General Theory of Quantized Fields”, Providence, R.I.: Publ. Amer. Math. Soc. 1965

    MATH  Google Scholar 

  26. F. Wilczek, Phys. Rev. Lett. 49, 957 (1982);

    Article  MathSciNet  Google Scholar 

  27. F. Wilczek and A. Zee, Phys. Rev. Lett. 51, 2250 (1983)

    Article  MathSciNet  Google Scholar 

  28. Y.-S. Wu, “Fractional Quantum Statistics in Two-Dimensional Systems”, in: Proc. 2nd Int. Symp. Foundations of Quantum Mechanics, Tokyo 1986, pp. 171–180, and refs. given there

    Google Scholar 

  29. J. Fröhlich and P.-A. Marchetti, “A Gauge Theory of Anyons”, Preprint 1988

    Google Scholar 

  30. S. Kind, diploma thesis, ETH 1988

    Google Scholar 

  31. D.A. Arovas, R. Schrieffer, F. Wilczek and A. Zee, Nucl. Phys. B 251 [FS 13] , 117 (1985)

    Article  MathSciNet  Google Scholar 

  32. S. Deser, R. Jackiw and G. Hooft, Ann. Phys. 152, 220 (1984);

    Article  Google Scholar 

  33. S. Giddings, J. Abbott and K. Kuchar, Gen. Rel. and Gray. 16, 751 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  34. R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983);

    Article  Google Scholar 

  35. B.I. Halperin, Phys. Rev. Lett. 52, 1583 (1984);

    Article  Google Scholar 

  36. D.A. Arovas, R. Schrieffer and F. Wilczek, Phys. Rev. Lett. 53, 722 (1984);

    Article  Google Scholar 

  37. R. Tao and Y.-S. Wu, Phys. Rev. B 31, 6859 (1985)

    Article  MathSciNet  Google Scholar 

  38. P.B. Wiegmann, “Super conductivity in Strongly Correlated Electronic Systems and Confinement vs. Deconfinement Phenomena”, Preprint 1987

    Google Scholar 

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Froehlich, J. (1988). Statistics and Monodromy in Two- and Three-Dimensional Quantum · Field Theory. In: Bleuler, K., Werner, M. (eds) Differential Geometrical Methods in Theoretical Physics. NATO ASI Series, vol 250. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7809-7_10

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  • DOI: https://doi.org/10.1007/978-94-015-7809-7_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8459-0

  • Online ISBN: 978-94-015-7809-7

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