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- Title
Renormalization group functions of the φ<sup>4</sup> theory in the strong coupling limit: Analytical results.
- Authors
Suslov, I. M.
- 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) = β∞ g 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.
- Subjects
CELESTIAL mechanics; MECHANICS (Physics); ASTROPHYSICS; PERTURBATION theory; DYNAMICS; FUNCTIONAL analysis
- Publication
Journal of Experimental & Theoretical Physics, 2008, Vol 107, Issue 3, p413
- ISSN
1063-7761
- Publication type
Article
- DOI
10.1134/S1063776108090094