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Renormalization group functions of the φ4 theory in the strong coupling limit: Analytical results

  • Nuclei, Particles, Fields, Gravitation, and Astrophysics
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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.

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  1. Kapitza Institute for Physical Problems, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russia

    I. M. Suslov

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Original Russian Text © I.M. Suslov, 2008, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 3, pp. 490–508.

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Suslov, I.M. Renormalization group functions of the φ4 theory in the strong coupling limit: Analytical results. J. Exp. Theor. Phys. 107, 413–429 (2008). https://doi.org/10.1134/S1063776108090094

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