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Progress in Gauge Field Theory pp 497–529Cite as

Guage Invariant Frequency Splitting in Non Abelian Lattice Guage Theory

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Part of the book series: NATO ASI Series ((NSSB,volume 115))

Abstract

Lattice gauge theory, the problem of quark confinement and renormalization group (RG) methods have constituted a central theme of this school. As is well known, quark confinement, the existence of a mass gap, etc., can be proved in pure 4-dimensional Euclidean lattice gauge theory for a sufficiently large coupling constant /1/. On the other hand, perturbative RG studies show asymptotic freedom at short distances.++ As K.G. Wilson has forcefully advocated over the years, the modern RG /2 / is essential to study the connection between the short and long distance behavior. Fortunately, the modern RG is slowly coming under mathematical control§, and it is to be hoped that in the not too distant future these methods will become powerful enough for the control of the most challenging and fascinating of renormalizable field theories: non-abelian gauge field theory in four dimensions.

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References

  1. K.G. Wilson, Phys. Rev. D10, 2445 (1974).

    ADS  Google Scholar 

  2. —, in: “New Developments in Quantum Field Theory and Statistical Mechanics,” M. Lévy and P.K. Mitter, eds., Plenum Press, N.Y. (1977). K. Osterwalder, ibid.

    Google Scholar 

  3. J. Drouffe and C. Itzykson, Phys. Rep. 38C (1978), 133.

    Article  MathSciNet  ADS  Google Scholar 

  4. K. Osterwalder and E. Seiler, Ann. Phys. 110, 440 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  5. E. Seiler: Lecture notes in Physics No. 159, Springer (1982).

    Google Scholar 

  6. K.G. Wilson and J. Kogut, Phys. Rep. C, 12 (1974), 75

    Article  ADS  Google Scholar 

  7. K.G. Wilson, Rev. Mod. Phys. 47 (1975), 773

    Article  ADS  Google Scholar 

  8. —, Rev. Mod. Phys. 55 (1983), 583

    Article  ADS  Google Scholar 

  9. —, in: “Recent Developments in Gauge Theories,” G. ‘tHooft et al, eds., Plenum Press, N.Y. (1980).

    Google Scholar 

  10. J.H. Lowenstein and P.K. Mitter, Ann. of Physics 105 (1977), 138.

    Article  ADS  Google Scholar 

  11. G. Valent, Thèse d’Etat (Université Paris VII, 1979).

    Google Scholar 

  12. P.K. Mitter, G. Valent, Phys. Lett. 70B (1977), 65.

    MathSciNet  ADS  Google Scholar 

  13. M. Göpfert and G. Mack, Comm. Math. Phys. 82 (1982), 545.

    Article  ADS  Google Scholar 

  14. J. Frbölich, Comm. Math. Phys. 47 (1976), 233.

    Article  MathSciNet  ADS  Google Scholar 

  15. D. Brydges, Coiran. Math. Phys. 58 (1978), 313.

    Article  MathSciNet  ADS  Google Scholar 

  16. G. de Rham, “Variétés différentiates,” Hermann, Paris (1960).

    Google Scholar 

  17. J.L. Koszul, Lectures on Fibre Bundles and Differential Geometry, Tata Institute of Fundamental Research, Bombay (1960).

    Google Scholar 

  18. S.S. Chern, “Complex Manifolds Without Potential Theory,”D. Van Nostrand, Princeton, N.J. (1967).

    MATH  Google Scholar 

  19. M. Atiyah and R. Bott, Yang-Mills fields on Riemann surfaces (to be published).

    Google Scholar 

  20. J. Glimm and A. Jaffe, Comm. Math. Phys 56 (1977), 195.

    Article  MathSciNet  ADS  Google Scholar 

  21. L. Gross, Convergence of U(1)3 lattice gauge theory to its continuum limit (to be published).

    Google Scholar 

  22. A. Guth, Phys. Rev. D21 (1980), 2291.

    MathSciNet  ADS  Google Scholar 

  23. G. Mack, Dielectric lattice gauge theory (DESY 83-052), to appear in Nuclear Physics B.

    Google Scholar 

  24. B. Sharpe, Gribov copies and the Faddeev-Popov formula in lattice gauge theories (to be published in Nuclear Physics B).

    Google Scholar 

  25. P. Hirschfeld, Nucl. Phys. B 157 (1978), 37.

    MathSciNet  ADS  Google Scholar 

  26. B.W. Lee and J. Zinn-Justin, Phys. Rev. D5 (1972), 3121.

    ADS  Google Scholar 

  27. K. Gawedski and A. Kupiainen, Comm. Math. Phys. 77_ (1980), 31.

    Article  MathSciNet  ADS  Google Scholar 

  28. K. Symanzik, in: “Recent Developments in Gauge Theories,” op.cit.

    Google Scholar 

  29. P. Breitenlohner and D. Maison, Comm. Math. Phys. 52: (1977), 11, 39, 55.

    Article  MathSciNet  ADS  Google Scholar 

  30. I.M. Singer, Comm. Math. Phys. 60 (1978), 7.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. M.S. Narasimhan and T.R. Ramadas, Comm. Math. Phys. 67 (1979), 21.

    Article  MathSciNet  Google Scholar 

  32. P.K. Mitter and C.M. Viallet, ibid., 79 (1981), 457.

    Google Scholar 

  33. M. Asorey and P.K. Mitter, CERN/TH 3424.

    Google Scholar 

  34. G. Gallavotti et al, Comm. Math. Phys. 59 (1978), 143; 71 (1980), 95.

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie (Paris VI), Tour 16, 1er étage, 4 Place Jussieu, 75230, Paris Cedex 05, France

    P. K. Mitter

Authors
  1. P. K. Mitter
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Physics, Utrecht, The Netherlands

    G. ’t Hooft

  2. Harvard University, Cambridge, Massachusetts, USA

    A. Jaffe

  3. University of Hamburg, Hamburg, Federal Republic of Germany

    H. Lehmann

  4. University of Paris VI, Paris, France

    P. K. Mitter

  5. University of California, Berkeley, California, USA

    I. M. Singer

  6. Laboratory of Particle Physics, Annecy, France

    R. Stora

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© 1984 Plenum Press, New York

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Mitter, P.K. (1984). Guage Invariant Frequency Splitting in Non Abelian Lattice Guage Theory. In: ’t Hooft, G., Jaffe, A., Lehmann, H., Mitter, P.K., Singer, I.M., Stora, R. (eds) Progress in Gauge Field Theory. NATO ASI Series, vol 115. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0280-4_17

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  • DOI: https://doi.org/10.1007/978-1-4757-0280-4_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0282-8

  • Online ISBN: 978-1-4757-0280-4

  • eBook Packages: Springer Book Archive

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