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Non Local Observables and Confinement in BF Formulation of Yang-Mills Theory

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Quantum Fields and Quantum Space Time

Part of the book series: NATO ASI Series ((NSSB,volume 364))

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Abstract

The vev’s of the magnetic order-disorder operators in QCD are found with an explicit calculation using the first order formulation of Yang-Mills theory.

Seminar presented by M. Martellini

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References

  1. A. A. Abrikosov, Soviet Phys. JEPT 5 (1957) 1174

    Google Scholar 

  2. H. B. Nielsen and P. Olesen, Nucl. Phys. B61 (1973) 45.

    Article  ADS  Google Scholar 

  3. S. Mandelstam, Phys.Rep. 23C(1976)245.

    Article  ADS  Google Scholar 

  4. G.’ t Hooft, in High Energy Physics, EPS International Conference, Palermo 1975, ed. A. Zichichi; Physica Scripta, 25(1982)133.

    Article  ADS  Google Scholar 

  5. A. M. Polyakov, “Gauge Fields and Strings”, Harwood Academic Publishers (Chur, Switzerland 1978).

    Google Scholar 

  6. G.’ t Hooft, Nucl. Phys. B138 (1978) 1; B153 (1979) 141.

    Article  ADS  Google Scholar 

  7. G.’ t Hooft, Nucl. Phys. B190 [FS3] (1981) 455.

    Article  ADS  Google Scholar 

  8. F. Fucito, M. Martellini and M. Zeni, “The BF formalism for QCD and Quark Confinement”, hep-th/9605018; “A new Nonperturbative Approach to QCD by BF Theory”, hep-th/9607044.

    Google Scholar 

  9. A. S. Cattaneo, P. Cotta-Ramusino, A. Gamba and M. Martellini, Phys. Lett. B355 (1995) 245

    ADS  Google Scholar 

  10. A. S. Cattaneo, P. Cotta-Ramusino, J. Fröhlich and M. Martellini, J. Math. Phys. 36 (1995) 6137.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. The first order formalism, leading to the so-called “field strength approach”, was first introduced by M. B. Halpern, Phys. Rev. D16 (1977) 1798; Phys. Rev. D16 (1977) 3515; Phys. Rev. D19 (1979) 517. For recent developments see H. Reinhardt, hep-th/9608191 and references therein.

    ADS  Google Scholar 

  12. Z.F. Ezawa and A. Iwazaki, Phys. Rev. D25 (1982) 2681; Phys.Rev. D26(1982)631.

    ADS  Google Scholar 

  13. G. Horowitz, Comm.Math.Phys. 125 (1989) 417

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. M. Blau and G. Thompson, Ann. Phys. 205 (1991) 130

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. N. Maggiore and S. P. Sorella, Int. J. Mod. Phys. A8 (1993) 929.

    MathSciNet  ADS  Google Scholar 

  16. M. Martellini and M. Zeni, “The BF Formalism for YM theory and the’ t Hooft algebra”, in proceeding of “Quark Confinement and Hadron Spectrum 96”, hep-th/9610090; “Diagrammatic Feynman rules and β-function for the BF approach to QCD”, in preparation.

    Google Scholar 

  17. I. Ya Araf’eva, Theor. Math. Phys. 43 (1980) 353

    Article  Google Scholar 

  18. N. Bralic, Phys. Rev. D22 (1980) 3090.

    MathSciNet  ADS  Google Scholar 

  19. F. Fucito, M. Martellini, A. Tanzini and M. Zeni, “The Topological Embedding of the BF Theory in Yang-Mills”, in preparation

    Google Scholar 

  20. G. Calugareanu, Revue de Math. Pures et Appl. (Bucarest) 4 (1959) 5

    MathSciNet  Google Scholar 

  21. W. F. Pohl, J. Math. Mech. 17 (1986) 975.

    MathSciNet  Google Scholar 

  22. G.’ t Hooft, Nucl.Phys. B35 (1971) 167.

    Article  ADS  Google Scholar 

  23. D. S. Freed and K. K. Uhlenbeck, “Instantons and Four Manifolds” Springer Verlag (NY 1984).

    Google Scholar 

  24. G.’ t Hooft, Nucl.Phys. B72 (1974) 461.

    ADS  Google Scholar 

  25. A. S. Kronfeld, G. Schierholz and U. J. Wiese, Nucl.Phys. B293 (1987) 461.

    Article  MathSciNet  ADS  Google Scholar 

  26. D. Anselmi and P. Fré, Phys. Lett. B347 (1994) 247.

    ADS  Google Scholar 

  27. E. Witten, Math. Research Lett. 1 (1994) 769.

    MathSciNet  MATH  Google Scholar 

  28. S. K. Donaldson and P. B. Kronheimer, “The Geometry of Four Manifolds”, Oxford Press (Oxford 1991).

    Google Scholar 

  29. T. R. Morris, D. A. Ross and C. T. Sachrajda, Nucl Phys. B255 (1985) 115

    Article  ADS  Google Scholar 

  30. H. Osborn, Ann.Phys. 135 (1981) 373.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. E. Corrigan, P. Goddard, H. Osborn and S. Templeton, Nucl. Phys. B159 (1979) 469.

    Article  MathSciNet  ADS  Google Scholar 

  32. P. Cotta-Ramusino and M. Martellini, in “Knots and Quantum Gravity”, Ed. J. Baez, Oxford University Press, Oxford NY (1994)

    Google Scholar 

  33. A. S. Cattaneo, “Teorie Topologiche di tipo BF ed Invarianti dei Nodi”, PhD-Thesis, University of Milan, Italy (1995).

    Google Scholar 

  34. G. T. Horowitz and M. Srednicki, Comm. Math. Phys. 130 (1990) 83.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Y. Makeenko, private communication.

    Google Scholar 

  36. A. M. Polyakov, “Confining Strings”, hep-th/9607049.

    Google Scholar 

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Fucito, F., Martellini, M., Zeni, M. (1997). Non Local Observables and Confinement in BF Formulation of Yang-Mills Theory. In: ’t Hooft, G., Jaffe, A., Mack, G., Mitter, P.K., Stora, R. (eds) Quantum Fields and Quantum Space Time. NATO ASI Series, vol 364. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1801-7_15

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  • DOI: https://doi.org/10.1007/978-1-4899-1801-7_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1803-1

  • Online ISBN: 978-1-4899-1801-7

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