2008/06/04 by I. M. Suslov, Suslov, I. M.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Relativity and Gravitational Theory #hep-ph
paper · pdf · doi:10.48550/arxiv.0806.0789
Latex, 14 pages, 3 figures included
arxiv created 2008/06/04 · openalex publication_date 2008/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The four-dimensional ϕ4 theory is usually considered to be trivial in the continuum limit. In fact, two definitions of triviality were mixed in the literature. The first one, introduced by Wilson, is equivalent to positiveness of the Gell-Mann -- Low function β(g) for g≠ 0; it is confirmed by all available information and can be considered as firmly established. The second definition, introduced by mathematical community, corresponds to the true triviality, i.e. principal impossibility to construct continuous theory with finite interaction at large distances: it needs not only positiveness of β(g) but also its sufficiently quick growth at infinity. Indications of true triviality are not numerous and allow different interpretation. According to the recent results, such triviality is surely absent.