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Asymptotic Series of Quantum Field Theory and Their Summation
Author(s) -
Kazakov D. I.,
Shirkov D. V.
Publication year - 1980
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19800280803
Subject(s) - path integral formulation , quantum field theory , series (stratigraphy) , sketch , perturbation theory (quantum mechanics) , mathematics , relation between schrödinger's equation and the path integral formulation of quantum mechanics , quantum gravity , saddle point , power series , quantum , field (mathematics) , quantum mechanics , physics , statistical physics , mathematical analysis , pure mathematics , geometry , paleontology , algorithm , biology
The problem of investigation of ultraviolet asymptotics in quantum field theory has met recently with specific difficulties related to the asymptotic character of power expansions of quantum perturbation theory. This article is a review on the present status of this problem. First, we discuss the saddle‐point method for the path integral, by which many important results have been obtained in the last years. Then a sketch of results is given concerning the asymptotic series in problems of quantum field theory and quantum mechanics. Next we consider the problem of “summation” of such series, which arises in attempting to reach the region of not small values of the coupling constant g .