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

Abstract

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.

PACS numbers

11.10.Gh 11.10.Hi 11.10.Jj 11.10.Kk 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

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

Personalised recommendations