Journal of Experimental and Theoretical Physics

, Volume 111, Issue 3, pp 450–465

Asymptotic behavior of the β function in the ϕ4 theory: A scheme without complex parameters

Order, Disorder, and Phase Transition in Condensed System

DOI: 10.1134/S1063776110090153

Cite this article as:
Suslov, I.M. J. Exp. Theor. Phys. (2010) 111: 450. doi:10.1134/S1063776110090153


The previously-obtained analytical asymptotic expressions for the Gell-Mann-Low function β(g) and anomalous dimensions in the ϕ4 theory in the limit g → ∞ are based on the parametric representation of the form g = f(t), β(g) = f1(t) (where tg0−1/2 is the running parameter related to the bare charge g0), which is simplified in the complex t plane near a zero of one of the functional integrals. In this work, it has been shown that the parametric representation has a singularity at t → 0; for this reason, similar results can be obtained for real g0 values. The problem of the correct transition to the strong-coupling regime is simultaneously solved; in particular, the constancy of the bare or renormalized mass is not a correct condition of this transition. A partial proof has been given for the theorem of the renormalizability in the strong-coupling region.

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

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

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