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arXiv · 1010.4317

Asymptotic Behavior of the \Beta Function in the \Phi^4 Theory: A Scheme Without Complex Parameters

Igor M. Suslov
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Abstract

The previously obtained analytical asymptotic expressions for the Gell-Mann - Low function \beta(g) and anomalous dimensions of \phi^4 theory in the limit g\to\infty are based on the parametric representation of the form g = f(t), \beta(g) = f1(t) (where t\sim g_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 the present paper, it is shown that the parametric representation has a singularity at t\to 0; for this reason, similar results can be obtained for real values of g_0. 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 is given for the theorem of the renormalizability in the strong coupling region.

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Igor M. Suslov. 2010-10-20. Asymptotic Behavior of the \Beta Function in the \Phi^4 Theory: A Scheme Without Complex Parameters. https://doi.org/10.1134/s1063776110090153

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