I.M.Suslov (P.L.Kapitza Institute for Physical Problems)

 

Renormalization group functions of \phi^4 theory in the strong coupling limit: analytical results.

 

Attempts of reconstruction of the \beta-function for \phi^4 theory, made previously by summation of perturbation series, lead to asymptotics \beta(g)=\beta_\infty g^\alpha for g\to\infty, where \alpha\approx 1 for space dimensions d=2,3,4. The natural hypothesis arises, that \beta(g) \sim g for large g at all d. Consideration of zero-dimensional case confirms this hypothesis and and reveals the mechanism of its origin: it is related with zeroing of one of functional integrals. It makes possble to generalize considerations to arbitrary d-dimensional case and confirm linear asymptotics for \beta-function at all d. Asymptotical behavior for anomalous dimensions is shown to be constant.