Related papers: How are Feynman graphs resumed by the Loop Vertex …

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non…

We summarize the Hopf algebra structure on Feynman diagrams and emphasize the interest in further algebraic structures hidden in Feynman graphs.

We study perturbative aspects of noncommutative field theories. This work is arranged in two parts. First, we review noncommutative field theories in general and discuss both canonical and path integral quantization methods. In the second…

We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all…

The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…

A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…

In this note, we introduce and study position space Feynman quadrics that are the loci of divergences of the position space Feynman integrals for Euclidean massless scalar quantum field theories. We prove that the Feynman quadrics define…

A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly)…

We summarize recent results connecting multiloop Feynman diagram calculations to different parts of mathematics, with special attention given to the Hopf algebra structure of renormalization.

Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the…

I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees…

A method is presented in which matrix elements for some processes are calculated recursively. This recursive calculational technique is based on the method of basis spinors.

Graphical functions are special position space Feynman integrals, which can be used to calculate Feynman periods and one- or two-scale processes at high loop orders. With graphical functions, renormalization constants have been calculated…

We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams…

With the aid of simple examples we show how to make simple estimates of the sizes of higher-order Feynman graphs. Our methods enable appropriate values of renormalization and factorization scales to be made. They allow the diagnosis of the…

Recently presented explicit formulae for asymptotic expansions of Feynman diagrams in the Sudakov limit are applied to typical two-loop diagrams. For a diagram with one non-zero mass these formulae provide an algorithm for analytical…

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of…

We describe the combinatorics that arise in summing a double recursion formula for the enumeration of connected Feynman graphs in quantum field theory. In one index the problem is more tractable and yields concise formulas which are…

A new kind of cut diagram is introduced to sum Feynman diagrams with nonabelian vertices. Unlike the Cutkosky diagrams which compute the discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent a resummation of both…

The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These equations, originating in the physics of 2-dimensional…