Hadron Structure and Lepton-Hadron Interactions pp 687-696 | Cite as

# Strong Interaction Models in 6-ɛ Dimensions

Chapter

## 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.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
- 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
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- 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
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- 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.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.E. Brézin, J.C. Le Guillou and J. Zinn-Justin, Phys. Rev. B10, (1974) 892.ADSCrossRefGoogle Scholar

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