Renormalization group functions of the φ4 theory in the strong coupling limit: Analytical results
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.
- Publication:
-
Soviet Journal of Experimental and Theoretical Physics
- Pub Date:
- September 2008
- DOI:
- 10.1134/S1063776108090094
- arXiv:
- arXiv:1010.4081
- Bibcode:
- 2008JETP..107..413S
- Keywords:
-
- 11.10.Gh;
- 11.10.Hi;
- 11.10.Jj;
- 11.10.Kk;
- Condensed Matter - Statistical Mechanics;
- High Energy Physics - Phenomenology;
- High Energy Physics - Theory
- E-Print:
- PDF, 17 pages