scholarly journals Ramanujan's Master Theorem applied to the evaluation of Feynman diagrams

2015 ◽  
Vol 63 ◽  
pp. 214-230 ◽  
Author(s):  
Ivan Gonzalez ◽  
Victor H. Moll ◽  
Ivan Schmidt
Keyword(s):  
Feynman Diagrams ◽  
Master Theorem

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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.

3-D Path Planning Using Subatomic Particles and Feynman Diagrams

2019 ◽  
Author(s):  
Julio F. Acosta ◽  
Victor H. Andaluz ◽  
Mauricio X. Naranjo ◽  
Jose I. Molina ◽  
Alex Santana G. ◽  
...  
Keyword(s):  
Path Planning ◽  
Feynman Diagrams ◽  
Subatomic Particles

Feynman Diagrams as Models

2017 ◽  
Vol 39 (2) ◽  
pp. 46-54 ◽  
Author(s):  
Michael Stöltzner
Keyword(s):  
Feynman Diagrams

Weight Systems from Feynman Diagrams

1998 ◽  
Vol 07 (01) ◽  
pp. 61-85 ◽  
Author(s):  
Dirk Kreimer
Keyword(s):  
Field Theory ◽  
Knot Theory ◽  
Feynman Diagrams ◽  
Weight System ◽  
Term Relation ◽  
Renormalization Theory

We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful association of renormalization theory with knot theory.

scholarly journals Feynman diagrams and rooted maps

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 149-167 ◽  
Author(s):  
Andrea Prunotto ◽  
Wanda Maria Alberico ◽  
Piotr Czerski
Keyword(s):  
Single Particle ◽  
Feynman Diagram ◽  
Feynman Diagrams ◽  
Topological Properties ◽  
Many Body ◽  
Perturbative Order ◽  
Original Definition ◽  
Many Body Systems ◽  
Definition Of ◽  
Particle Propagator

Abstract The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.

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