scholarly journals Asymptotic expansions of Feynman diagrams and the Mellin-Barnes representation

2007 ◽  
Vol 164 ◽  
pp. 199-202
Author(s):  
Samuel Friot ◽  
David Greynat
Keyword(s):  
Asymptotic Expansions ◽  
Feynman Diagrams

scholarly journals FEYNMAN DIAGRAMS VIA GRAPHICAL CALCULUS

2002 ◽  
Vol 11 (07) ◽  
pp. 1095-1131 ◽  
Author(s):  
DOMENICO FIORENZA ◽  
RICCARDO MURRI
Keyword(s):  
Quantum Gravity ◽  
Asymptotic Expansions ◽  
Feynman Diagrams ◽  
Ribbon Graphs ◽  
Graphical Calculus

We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable family of graphs. We discuss how different kinds of interactions give rise to different families of graphs. In particular, we show how symmetric and cyclic interactions lead to "ordinary" and "ribbon" graphs respectively. As an example, the 't Hooft-Kontsevich model for 2D quantum gravity is treated in some detail.

scholarly journals ASYMPTOTIC EXPANSIONS IN MOMENTA AND MASSES AND CALCULATION OF FEYNMAN DIAGRAMS

1995 ◽  
Vol 10 (21) ◽  
pp. 1485-1499 ◽  
Author(s):  
V.A. SMIRNOV
Keyword(s):  
Asymptotic Expansions ◽  
Feynman Diagrams

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

scholarly journals EUCLIDEAN ASYMPTOTIC EXPANSIONS OF GREEN FUNCTIONS OF QUANTUM FIELDS (II) COMBINATORICS OF THE AS OPERATION

1993 ◽  
Vol 08 (13) ◽  
pp. 2241-2286 ◽  
Author(s):  
G. B. PIVOVAROV ◽  
F. V. TKACHOV
Keyword(s):  
Asymptotic Expansions ◽  
Short Distance ◽  
Feynman Diagrams ◽  
Operator Product ◽  
Green Functions ◽  
Small Parameters ◽  
Combinatorial Technique ◽  
Ms Scheme ◽  
The Masses ◽  
Distance Operator

The results of Ref. 1 are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS scheme in the regimes when some of the masses and external momenta are large with respect to the others. The large momenta are Euclidean, and the expanded diagrams are regarded as distributions with respect to them. The small masses may be equal to zero. The As operation for integrals is defined and a simple combinatorial technique is developed to study its exponentiation. The As operation is used to obtain the corresponding expansions of arbitrary Green functions. Such expansions generalize and improve upon the well-known short-distance, operator-product expansions, the decoupling theorem etc.: e.g. the low-energy effective Lagrangians are obtained to all orders of the inverse heavy mass. The obtained expansions possess the property of perfect factorization of large and small parameters, which is essential for meaningful applications to phenomenology. As an auxiliary tool, the inversion of the R operation is constructed. The results are valid for arbitrary QFT models.

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.

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