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Strong Interaction Models in 6-ɛ Dimensions

  • D. J. Wallace
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 39)

Abstract

A unique theory of the strong interactions can arise as a critical phenomenon with respect to some fundamental length scale. We discuss models which give a concrete realisation of this idea through ɛ-expansions in 6-ɛ dimensions. Illustrative calculations and problems in this approach are reviewed.

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References

  1. 1.
    These ideas and some calculations in 4-ɛ dimensional space time are reviewed in K.G. Wilson and J. Kogut, Phys. Reports, 12C, (1974) 75. See also S. Weinberg in Proceedings of the International School of Sub-Nuclear Physics, Ettore Majorana, 1976, and S.S. Shei and T. Yan, Phys. Rev. D8, (1973) 2457.ADSCrossRefGoogle Scholar
  2. 2.
    For reviews of the renormalization group in critical phenomena see for example, S.K. Ma, Modern Theory of Critical Phenomena, (W.A. Benjamin, Inc., Reading, Mass., 1976 ); E. Brézin, J.C. Le Guillou and J. Zinn-Justin in Phase Transitions and Critical Phenomena, Vol. 6, eds. C. Domb and M.S. Green (Academic Press, 1976), and other articles in that volume; M.E. Fisher, Rev. Mod. Phys. 46, (1974) 597; K.G. Wilson, Rev. Mod. Phys. 47, (1975) 773.Google Scholar
  3. 3.
    For example the non-polynomial Lagrangian approach is discussed in C.J. Isham, A. Salam and J. Strathdee, Phys. Rev. D5, (1972) 2548.ADSMathSciNetGoogle Scholar
  4. 4.
    H. Georgi, H.R. Quinn and S. Weinberg, Phys. Rev. Letters, 33, (1974) 451, give an example of renormalization effects at momentum scales infrared with respect to super-heavy vector boson masses.ADSCrossRefGoogle Scholar
  5. 5.
    J.C. Le Guillou and J. Zinn-Justin, Phys. Rev. Letters 39 (1977) 95ADSCrossRefGoogle Scholar
  6. 6.
    A.J. McKane, D.J. Wallace and R.K.P. Zia, Phys. Letters 65B, (1976) 171ADSCrossRefGoogle Scholar
  7. 7.
    A.J. McKane, J. Phys. G.Google Scholar
  8. 8.
    A.J. McKane and D.J. Wallace, to be published.Google Scholar
  9. 9.
    Expansions in 6-ɛ dimensions are studied in many critical phenomena. See e. g., A.B. Harris, T.C. Lubensky, W.K. Holcomb and C. Dasgupta, Phys. Rev. Letters 35 (1975) 327, E 1937; R.G. Priest and T.C. Lubensky Phys. Rev. B13, (1976) 4159 and Erratum; D.J. Amit, J. Phys. A9 (1976) 1441; A.B. Harris, T.C. Lubensky and J.H. Chen, Phys. Rev. Letters 36 (1976) 415. Many of these problems involve n →0 limits which can evade the diseases discussed in section 4.ADSCrossRefGoogle Scholar
  10. 10.
    G. Mack in Proceedings of the International Summer Institute on Theoretical Physics, Kaiserslautern, 1972, ed. J. Ehlers, K. Hepp and H.A. Weidenmuller ( Springer Verlag, Berlin, 1973 ), p. 300.Google Scholar
  11. 11.
    This number was also calculated, for different reasons, by S. Panfil, Contributed Paper, 1976 International Conference on High Energy Physics, Tbilisi.Google Scholar
  12. 12.
    D.J. Gross and H. Wilczek, Phys. Rev. Letters 30 (1973) 1343; H.D. Politzer, Phys. Rev. Letters 30 (1973)1346; S. Coleman and D.J. Gross, Phys. Rev. Letters 31 (1973) 1851. For a recent phenomenological fit and further references see the lectures by C.H. Llewellyn-Smith.ADSCrossRefGoogle Scholar
  13. 13.
    E. Brézin, J.C. Le Guillou and J. Zinn-Justin, Phys. Rev. B10, (1974) 892.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • D. J. Wallace
    • 1
  1. 1.Department of PhysicsThe University SouthamptonEngland

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