I.M.Suslov. Triviality, Renormalizability and Confinement

Natural Sciences / Physics / Mathematical Physics

Submitted on: Oct 06, 2012, 08:45:00

Description: According to recent results, the Gell-Mann - Low function beta(g) of four-dimensional phi^4 theory is non-alternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means possibility to construct the continuous theory with finite interaction at large distances. This conclusion is in visible contradiction with the lattice results indicating triviality of phi^4 theory. This contradiction is resolved by a special character of renormalizability in phi^4 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 as solved, at least on the physical level of rigor.

The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.

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