Application of conformal mapping and Padé approximants (ωP′s) to the calculation of various two-loop Feynman diagrams

1994 ◽  
Vol 37 (2) ◽  
pp. 115-119 ◽  
Author(s):  
J. Fleischer ◽  
O.V. Tarasov
Keyword(s):  
Conformal Mapping ◽  
Padé Approximants ◽  
Feynman Diagrams ◽  
Pade Approximants

CALCULATION OF TWO-LOOP VERTEX FUNCTIONS FROM THEIR SMALL MOMENTUM EXPANSION

1995 ◽  
Vol 06 (04) ◽  
pp. 495-501 ◽  
Author(s):  
J. FLEISCHER
Keyword(s):  
Conformal Mapping ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Padé Approximants ◽  
Feynman Diagrams ◽  
Powerful Method ◽  
Small Momentum ◽  
Numerical Examples ◽  
Pade Approximants

In a recent paper1 a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared, a certain conformal mapping and subsequent resummation by means of Padé approximants. I present numerical examples.

scholarly journals Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams

1997 ◽  
Vol 56 (11) ◽  
pp. 6980-6992 ◽  
Author(s):  
Stanley J. Brodsky ◽  
John Ellis ◽  
Einan Gardi ◽  
Marek Karliner ◽  
Mark A. Samuel
Keyword(s):  
Padé Approximants ◽  
Feynman Diagrams ◽  
Pade Approximants

Numerical Evaluation of Partial Wave Contributions to Pion–Nucleon Amplitudes

1974 ◽  
Vol 52 (8) ◽  
pp. 731-742 ◽  
Author(s):  
Robert C. Brunet
Keyword(s):  
Partial Wave ◽  
Fourth Order ◽  
Numerical Evaluation ◽  
Padé Approximants ◽  
Feynman Diagrams ◽  
Order Perturbation ◽  
Pade Approximants ◽  
Pion Nucleon ◽  
Low Order

We present detailed numerical evaluations of the partial wave projections of Feynman diagrams of second- and fourth-order in perturbation for the πN–πN scattering in the [Formula: see text] theory. Perturbative contributions to the S, P, and D waves of isospin 1/2 and 3/2 are given in tables of numerical values. Figures regrouping these results show surprising behavior for the ratios Re(4)/Re(2). These tables and figures allow easy calculations with models using low order perturbation terms such as Padé approximants.

Conformal mapping, Padé approximants, and an example of flow with a significant deformation of the free boundary

2014 ◽  
Vol 25 (6) ◽  
pp. 729-747 ◽  
Author(s):  
E. A. KARABUT ◽  
A. A. KUZHUGET
Keyword(s):  
Velocity Field ◽  
Free Boundary ◽  
Power Series ◽  
Conformal Mapping ◽  
Incompressible Fluid ◽  
Padé Approximants ◽  
Ideal Incompressible Fluid ◽  
Inertial Motion ◽  
Pade Approximants ◽  
Summation Of Series

A problem of plane inertial motion of an ideal incompressible fluid with a free boundary, which initially has a quadratic velocity field, is studied by semi-analytical methods. A conformal mapping of the domain occupied by the fluid onto a unit circle is sought in the form of a power series with respect to time. Summation of series is performed by using Padé approximants.

scholarly journals Padé approximants for the ground-state energy of closed-shell quantum dots

1997 ◽  
Vol 56 (24) ◽  
pp. 15740-15743 ◽  
Author(s):  
Augusto Gonzalez ◽  
Bart Partoens ◽  
François M. Peeters
Keyword(s):  
Quantum Dots ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Closed Shell ◽  
Padé Approximants ◽  
Pade Approximants
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