Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory

2000 ◽  
Vol 123 (3) ◽  
pp. 792-800 ◽  
Author(s):  
V. V. Belokurov ◽  
Yu. P. Solov'ev ◽  
E. T. Shavgulidze
Keyword(s):  
Perturbation Theory ◽  
Convergent Series ◽  
Divergent Series ◽  
Physical Quantities

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

scholarly journals Convergent perturbation theory for lattice models with fermions

2016 ◽  
Vol 31 (13) ◽  
pp. 1650072 ◽  
Author(s):  
V. K. Sazonov
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Expansions ◽  
Lattice Model ◽  
Lattice Models ◽  
Convergent Series ◽  
Standard Perturbation Theory

The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.

scholarly journals New series representations for the two-loop massive sunset diagram

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
B. Ananthanarayan ◽  
Samuel Friot ◽  
Shayan Ghosh
Keyword(s):  
Perturbation Theory ◽  
Standard Model ◽  
Analytic Continuation ◽  
Chiral Perturbation Theory ◽  
Convergent Series ◽  
Regions Of Interest ◽  
External Momentum ◽  
Chiral Perturbation ◽  
Physical Problems ◽  
Series Representations

Abstract We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses $$m_1,\, m_2$$m1,m2 and $$m_3$$m3 and external momentum p by techniques of analytic continuation on a well-known triple series that corresponds to the Lauricella $$F_C^{(3)}$$FC(3) function. The convergence regions of the new series contain regions of interest to physical problems. These include some ranges of masses and squared external momentum values which make them useful from Chiral Perturbation Theory to some regions of the parameter space of the Minimal Supersymmetric Standard Model. The analytic continuation results presented for the Lauricella series could be used in other settings as well.

scholarly journals VII. A theory of asymptotic series

1912 ◽  
Vol 211 (471-483) ◽  
pp. 279-313 ◽  
Keyword(s):  
Power Series ◽  
Mathematical Analysis ◽  
Asymptotic Series ◽  
Convergent Series ◽  
Divergent Series ◽  
Consistent Theory

In their efforts to place mathematical analysis on the firm est possible foundations, Abel and Cauchy found it necessary to banish non-convergent series from their work ; from that time until a quarter of a century ago the theory o f divergent series was, in general, neglected by mathematicians. A consistent theory of divergent series was, however, developed by Poincaré in 1886, and, ten years later, Borel enunciated his theory of summability in connection with oscillating series. So far as diverging power series are concerned, the theory of Borel is more precise than that of Poincaré.

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