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Journal of Experimental and Theoretical Physics

, Volume 111, Issue 3, pp 450–465 | Cite as

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

  • I. M. Suslov
Order, Disorder, and Phase Transition in Condensed System

Abstract

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) = f 1(t) (where tg 0 −1/2 is the running parameter related to the bare charge g 0), 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 g 0 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.

Keywords

Real Axis Anomalous Dimension Functional Integral Renormalization Scheme Strong Coupling Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

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

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