Abstract
According to recent results, the Gell-Mann-Low function β(g) of four-dimensional φ4 theory is nonalternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means the possibility of constructing a continuous theory with finite interaction at large distances. This conclusion is in visible contradiction to the lattice results indicating triviality of φ4 theory. This contradiction is resolved by a special character of renormalizability in φ4 theory: to obtain the continuous renormalized theory, there is no need to eliminate a lattice from the bare theory. In fact, such kind of renormalizability is not accidental and can be understood in the framework of Wilson’s many-parameter renormalization group. Application of these ideas to QCD shows that Wilson’s theory of confinement is not purely illustrative, but has a direct relation to a real situation. As a result, the problem of analytical proof of confinement and a mass gap can be considered solved, at least on the physical level of rigor.
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Original Russian Text © I.M. Suslov, 2011, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2011, Vol. 140, No. 4, pp. 712–721.
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Suslov, I.M. On Wilson’s theory of confinement. J. Exp. Theor. Phys. 113, 619–627 (2011). https://doi.org/10.1134/S106377611109010X
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DOI: https://doi.org/10.1134/S106377611109010X