scholarly journals Massive 3-loop Feynman diagrams reducible to SC $^*$ primitives of algebras of the sixth root of unity

1999 ◽  
Vol 8 (2) ◽  
pp. 311-333 ◽  
Author(s):  
D.J. Broadhurst
Keyword(s):  
Feynman Diagrams ◽  
Root Of Unity

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

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

scholarly journals p-adic confluence of q-difference equations

2008 ◽  
Vol 144 (4) ◽  
pp. 867-919 ◽  
Author(s):  
Andrea Pulita
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Root Of Unity

AbstractWe develop the theory of p-adic confluence of q-difference equations. The main result is the fact that, in the p-adic framework, a function is a (Taylor) solution of a differential equation if and only if it is a solution of a q-difference equation. This fact implies an equivalence, called confluence, between the category of differential equations and those of q-difference equations. We develop this theory by introducing a category of sheaves on the disk D−(1,1), for which the stalk at 1 is a differential equation, the stalk at q isa q-difference equation if q is not a root of unity, and the stalk at a root of unity ξ is a mixed object, formed by a differential equation and an action of σξ.

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.

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