scholarly journals Perturbation theory and higher order $\mathcal{S}^{\!p}$-differentiability of operator functions

2021 ◽  
Author(s):  
Clément Coine
Keyword(s):  
Perturbation Theory ◽  
Higher Order ◽  
Operator Functions

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.

Aspects of the weak-coupling theory of open systems

1983 ◽  
Vol 61 (11) ◽  
pp. 1479-1485 ◽  
Author(s):  
I. D. Cox ◽  
W. E. Hagston ◽  
B. J. Holmes
Keyword(s):  
Perturbation Theory ◽  
Open System ◽  
Weak Coupling ◽  
Open Systems ◽  
Higher Order ◽  
Projection Operators ◽  
Coupling Theory ◽  
Weak Coupling Theory ◽  
Damping Theory ◽  
Insight Into

Damping theory of an open system S is usually formulated in terms of projection operators which introduce nonuniqueness into the analysis. An insight into the nature of the approximations that arise from this aspect of the formalism is revealed by considering systems of varying complexity. This leads to the conclusion that the results of higher order perturbation theory approximations may not be meaningful.

Higher order conformal perturbation theory

2009 ◽  
Vol 57 (5-7) ◽  
pp. 678-683
Author(s):  
C. Schmidt-Colinet
Keyword(s):  
Perturbation Theory ◽  
Higher Order

scholarly journals PERTURBATIVE EXPANSION OF τ HADRONIC SPECTRAL FUNCTION MOMENTS

2014 ◽  
Vol 35 ◽  
pp. 1460442
Author(s):  
DIOGO BOITO
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Systematic Study ◽  
Higher Order ◽  
Perturbative Expansion ◽  
Main Stream ◽  
Spectral Functions ◽  
Perturbative Series ◽  
Fixed Order ◽  
Adler Function

In the extraction of αs from hadronic τ decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of αs. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The yet unknown higher order coefficients of the perturbative series were modelled using the available knowledge of the renormalon singularities of the QCD Adler function. We were able to show that within these RGI frameworks some of the commonly employed moments should be avoided due to their poor perturbative behavior. Furthermore, under reasonable assumptions about the higher order behavior of the perturbative series FOPT provides the preferred RGI framework.

scholarly journals Higher-order Lagrangian perturbative theory for the Cosmic Web

2014 ◽  
Vol 11 (S308) ◽  
pp. 119-120
Author(s):  
Takayuki Tatekawa ◽  
Shuntaro Mizuno
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Initial Conditions ◽  
Higher Order ◽  
Order Perturbation ◽  
Initial Condition ◽  
The Difference ◽  
Fifth Order ◽  
The Universe ◽  
Higher Order Lagrangian

AbstractZel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

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