2008/04/02 by I. M. Suslov, Suslov, I. M.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum chaos and dynamical systems #advanced mathematical theories #cond-mat.stat-mech #hep-ph #hep-th
paper · pdf · doi:10.48550/arxiv.0804.0368
Latex, 16 pages, 2 figures included
arxiv created 2010/10/16 · arxiv updated 2010/10/19
Reconstruction of the β-function for ϕ4 theory, attempted previously by summation of perturbation series, leads to asymptotics β(g)=β_∞ gαat g→∞, where α≈ 1 for space dimensions d=2,3,4. The natural hypothesis arises, that asymptotic behavior is β(g) ∼ g for all d. Consideration of the zero-dimensional case confirms the hypothesis and reveals the origin of this result: it is related with a zero of a certain functional integral. Consideration can be generalized to the arbitrary space dimensionality, confirming the linear asymptotics of β(g) for all d. Asymptotical behavior for other renormalization group functions (anomalous dimensions) is found to be constant. Relation to the "zero charge" problem is discussed.