Strong Interaction Models in 6-ɛ Dimensions
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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- 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.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
- 7.A.J. McKane, J. Phys. G.Google Scholar
- 8.A.J. McKane and D.J. Wallace, to be published.Google Scholar
- 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.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.This number was also calculated, for different reasons, by S. Panfil, Contributed Paper, 1976 International Conference on High Energy Physics, Tbilisi.Google Scholar