Electric and Magnetic Confinement Schemes

  • F. Englert
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 39)


The theory of confinement is addressed to a paradoxical situation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    The “dual string” interpretation of dual phenomenology and in particular of rising Regge trajectories was introduced by Nambu, Nielsen, Susskind and Takabayashi in 1970. For a comprehensive study of “dual strings” and of their application to dual models sea. C. Rebbi, Physics Reports 12C, n° 1 (1974). S. Mandelstam, Physics Reports 13C, n°6 (1974).ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    J. Bardeen, L.N. Cooper and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957). An approach to the B.C.S. theory closer to the field theoretical analysis is given by Y. Nambu Phys. Rev. 117, 648 (1959).ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    Y. Nambu and L. Jona-Lasinio, Phys. Rev. 122, 345 ( 1961 ). For applications of the Nambu-Goldstone theorem in statistical mechanics see R. Brout “Phase Transitions” W.A. Benjamin Inc. New York (1963).Google Scholar
  4. 4.
    F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964). F. Englet, R. Brout and M-F Thiry, II N. Cimento, 43, 244 (1966).ADSCrossRefGoogle Scholar
  5. 5.
    V.L. Ginzburg and L.D. Landau. 20, 1064 (1950). For the application of the Ginzburg-Landau formalism in type II superconductors and in particular to the flux tubes discovered by Abrikosov (A.A. Abrikoxov, Zh. Eksp. i. Th. Fiz. 32, 1442 (1957) see A.L. Fetter and P.C. Hohenberg “Theory of type II superconductors” in “Superconductivity” Vol. II pp. 817, Edited by R.D. Parks; M. Dekker Inc., New York (1969).Google Scholar
  6. 6.
    P.W. Higgs, Phys. Letters 12, 132 (1964); Phys. Rev. Letters 13, 508 (1964), Phys. Rev. 145, 1156 (1966).ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    One could equivalent restrict the domain of validity of \(\vec \nabla \,x\,\vec \nabla \chi \) outside the axis and give up Stokes’ theorem. The al-ternate approach presented here makes contact with the Dirac string procedure (see chapter III), it was suggested to me by J. Nuyts. See also R. Brout “Flux Line and Monopole Mechanisms of Confinement” Symposium on Dynamical Broken Symmetry I.C.T.P. Trieste (1976).Google Scholar
  8. 8.
    B. Nielsen and P.O. Olesen, Nucl. Phys. B61, 45 (1973).ADSCrossRefGoogle Scholar
  9. 9.
    Y. Nambu, Phys. Rev. D10, 4262 (1974).ADSCrossRefGoogle Scholar
  10. 10.
    P.A.M. Dirac, Phys. Rev. 74, 817 (1948).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    T.T. Wu and C.N. Yang, Phys. Rev. D12, 3845 (1975).ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    Z.F. Ezawa and H.C. Tze, Phys. Rev. D15, 1647 (1977).ADSMathSciNetGoogle Scholar
  13. 13.
    S. Arafune, P.G.O. Freund and C.S. Goebel, J. Math. Phys. 16, 433 (1975).ADSCrossRefMathSciNetGoogle Scholar
  14. 14.
    T.T. Wu and C.N, Yang, “Properties of Hatter under Unusual Conditions” p. 349 Interscience (1969).Google Scholar
  15. 15.
    F. Englert and P. Windey, Phys. Rev. D14, 2728 (1976).ADSMathSciNetGoogle Scholar
  16. 16.
    See for instance D. Speiser in “Group Theoretical Concepts and Methods in Elementary Particle Physics” Edited by F. Gursey — Gordon and Breach, New York (1964).Google Scholar
  17. 17.
    G. ’t Hooft, Nucl. Phys. B79, 276 (1974). A.M. Polyakov, Zh. Eksp. Theor. Fiz. 20, 403 (1974). (J.E.T.P. Lett. 20, 199 (1974).Google Scholar
  18. 18.
    M.K. Prasad and C.M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975).ADSCrossRefGoogle Scholar
  19. 19.
    E.J. Weinberg and A.H. Guth, Phys. Rev. D14, 1660 (1976).ADSCrossRefGoogle Scholar
  20. 20.
    F.A. Bais and J.R. Primack, to be published in Nucl. Phys. B.Google Scholar
  21. 21.
    A general discussion of topological stability is given in S. Coleman. “Classical Lumps and their Quantum Descendants”, Lectures at the 1975 Erice Summer School, Harvard preprint (December 1975).Google Scholar
  22. 22.
    N.H. Christ, Phys. Rev. Lett. 34, 355 (1975).ADSCrossRefMathSciNetGoogle Scholar
  23. 23.
    A.M. Polyakov, Phys. Lett. 59B, 82 (1975).CrossRefMathSciNetGoogle Scholar
  24. 24.
    A.M. Polyakov, Nordita Preprint 76 /33 (1976).Google Scholar
  25. 25.
    G. ’t Hooft, Phys. Rev. Lett. 37, 8 (1976). C.G. Callan, R.F. Dashen and D.J. Gross, Phys. Lett. 63B, 334 (1976).CrossRefGoogle Scholar
  26. 26.
    C.G. Callan, R.F. Dashen and D.J. Gross, Phys. Lett. 66D, 375 (1977).CrossRefGoogle Scholar
  27. 27.
    A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Yu. S. Tyupkin, Phys. Lett. 59B, 85 (1975).CrossRefMathSciNetGoogle Scholar
  28. 28.
    G. Parisi, Phys. Rev. D11, 970 (1975).ADSGoogle Scholar
  29. 29.
    R. Brout, F. Englert and W. Fischler, Phys. Rev. Lett. 36, 649 (1976).ADSCrossRefGoogle Scholar
  30. 30.
    S. Mandelstam, Phys. Lett. 476 (1975).Google Scholar
  31. 31.
    G. ’t Hooft, Marseille Conference on Gauge Theories, (1972) (unpublished); H.D. Politzer Phys. Rev. Lett. 30, 1346 (1973) D.G. Gross and F. Wilczek, Phys. Rev. Lett., 30, 1343 (1973).ADSCrossRefGoogle Scholar
  32. 32.
    J. Kogut and L. Susskind, Phys. Rev. D9, 3501 (1974).ADSGoogle Scholar
  33. 33.
    L. Susskind, Bonn Summer School Lectures 1975. This paper contains also a review of the lattice gauge theories.Google Scholar
  34. 34.
    K.G. Wilson, Phys. Rev. D10, 2445 (1974).ADSCrossRefGoogle Scholar
  35. 35.
    J. Kogut and L. Susskind, Phys. Rev. D11, 395 (1975).ADSCrossRefMathSciNetGoogle Scholar
  36. 36.
    F. Englert and P. Windey: “Electric confinement and magnetic superconductors”, to be published. For detailed discussions on these problems, see P. Windey, PHD. Thesis — Université Libre de Bruxelles, (1977).Google Scholar
  37. 37.
    In principle, gauge fixing terms should be included in the functional integrand V.12). We shall ignore this inessential complication as those terms do not affect the semi-classical results of the following section.Google Scholar
  38. 38.
    The suggestion that monopoles could lead to an electric Meissner effect was made by S. Mandelstam at the Paris Meeting on Extended Systems in Field Theories (1975).Google Scholar
  39. 39.
    S.L. Adler, Phys. Rev. 137B, 1022 (1965).ADSCrossRefMathSciNetGoogle Scholar
  40. 40.
    M. Ademollo, G. Veneziano and S.Weinberg, Phys. Rev. Lett. 22, 83 (1969).ADSCrossRefGoogle Scholar
  41. 41.
    R. Brout, F. Englert and C. Truffin, Phys. Lett. 29B 590 (1969) 29B 686 (1969); F. Englert, R. Brout and H. Stern, Il Nuovo Cimento, 66, 845 (1969); R. Brout, F. Englert and C. Truffin, Phys. Rev. D9, 2694 (1974).ADSGoogle Scholar
  42. 42.
    G. ’t Hooft, Nucl. Phys. B75, 461 (1974).ADSGoogle Scholar
  43. 43.
    J.C. Pati and A. Salam, Phys. Rev. D8, 1240 (1973).ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • F. Englert
    • 1
  1. 1.Faculté des SciencesUniversité Libre de BruxellesBruxellesBelgium

Personalised recommendations