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
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.
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.
For example the non-polynomial Lagrangian approach is discussed in C.J. Isham, A. Salam and J. Strathdee, Phys. Rev. D5, (1972) 2548.
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.
J.C. Le Guillou and J. Zinn-Justin, Phys. Rev. Letters 39 (1977) 95
A.J. McKane, D.J. Wallace and R.K.P. Zia, Phys. Letters 65B, (1976) 171
A.J. McKane, J. Phys. G.
A.J. McKane and D.J. Wallace, to be published.
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.
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.
This number was also calculated, for different reasons, by S. Panfil, Contributed Paper, 1976 International Conference on High Energy Physics, Tbilisi.
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.
E. Brézin, J.C. Le Guillou and J. Zinn-Justin, Phys. Rev. B10, (1974) 892.
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Wallace, D.J. (1979). Strong Interaction Models in 6-ɛ Dimensions. In: Lévy, M., Basdevant, JL., Speiser, D., Weyers, J., Gastmans, R., Zinn-Justin, J. (eds) Hadron Structure and Lepton-Hadron Interactions. NATO Advanced Study Institutes Series, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2883-4_15
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