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

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 t ∞ 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 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. © 2010 Pleiades Publishing, Ltd.