Mathematical analysis of quantum fields—Historical survey and a new asymptotic perturbation theory

2021 ◽  
Vol 34 (1) ◽  
pp. 93-121
Author(s):  
Asao Arai
Keyword(s):  
Perturbation Theory ◽  
Mathematical Analysis ◽  
Historical Survey ◽  
Quantum Fields ◽  
Asymptotic Perturbation

scholarly journals Degenerate asymptotic perturbation theory

1983 ◽  
Vol 90 (2) ◽  
pp. 219-233 ◽  
Author(s):  
W. Hunziker ◽  
C. A. Pillet
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Perturbation

scholarly journals SYSTEMATIC SEARCH OF EXACTLY SOLVABLE NON-CENTRAL POTENTIALS

2005 ◽  
Vol 20 (05) ◽  
pp. 355-361 ◽  
Author(s):  
B. GÖNÜL ◽  
M. KOÇAK
Keyword(s):  
Perturbation Theory ◽  
Mathematical Analysis ◽  
Systematic Search ◽  
Exact Solvability ◽  
Exactly Solvable ◽  
Present Formalism

Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis of the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the effectiveness of the present formalism.

scholarly journals Extrapolation of perturbation-theory expansions by self-similar approximants

2014 ◽  
Vol 25 (5) ◽  
pp. 595-628 ◽  
Author(s):  
S. GLUZMAN ◽  
V.I. YUKALOV
Keyword(s):  
Perturbation Theory ◽  
Approximation Theory ◽  
Asymptotic Expansions ◽  
Applied Mathematics ◽  
Self Similar ◽  
Similar Approximation ◽  
Asymptotic Perturbation

The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.

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