Journal of Experimental and Theoretical Physics

, Volume 107, Issue 3, pp 413–429

Renormalization group functions of the φ4 theory in the strong coupling limit: Analytical results

Nuclei, Particles, Fields, Gravitation, and Astrophysics

DOI: 10.1134/S1063776108090094

Cite this article as:
Suslov, I.M. J. Exp. Theor. Phys. (2008) 107: 413. doi:10.1134/S1063776108090094


The previous attempts of reconstructing the Gell-Mann-Low function β(g) of the φ4 theory by summing perturbation series give the asymptotic behavior β(g) = βg in the limit g→∞, where α = 1 for the space dimensions d = 2, 3, 4. It can be hypothesized that the asymptotic behavior is β(g) ∼ g for all d values. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with vanishing of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior β(g) ∼ g in the general d-dimensional case. The asymptotic behaviors of other renormalization group functions are constant. The connection with the zero-charge problem and triviality of the φ4 theory is discussed.

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© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Kapitza Institute for Physical ProblemsRussian Academy of SciencesMoscowRussia