Related papers: Feynman amplitudes and Landau singularities for 1-…

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast…

It is by now well established that, by means of the integration by part identities, all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is…

Reduction techniques, Landau singularities and differential equations for Feynman amplitudes are briefly reviewed.

This article introduces moduli spaces of coloured graphs on which Feynman amplitudes can be viewed as 'discrete' volume densities. The basic idea behind this construction is that these moduli spaces decompose into disjoint unions of open…

Within the non-perturbative 1/N expansion, we discuss numerical methods for calculating multi-loop Feynman graph needed to derive physical scattering amplitudes. We apply higher order 1/N methods to the scalar sector of the standard model,…

Recently, we proposed a new approach for calculating Feynman graphs amplitude using the Gaussian representation for propagators which was proven to be exact in the limit of graphs having an infinite number of loops. Regge behavior was also…

This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining…

The general lines of the derivation and the main properties of the master equations for the master amplitudes associated to a given Feynman graph are recalled. Some results for the 2-loop self-mass graph with 4 propagators are then…

Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…

We derive a minimal set of Feynman rules for the loop amplitudes in unitary models of closed strings, whose target space is a simply laced (extended) Dynkin diagram. The string field Feynman graphs are composed of propagators, vertices…

In this talk we discuss how ideas from the theory of mixed Hodge structures can be used to find differential equations for Feynman integrals. In particular we discuss the two-loop sunrise graph in two dimensions and show that these methods…

We present a method to evaluate numerically Feynman diagrams directly from their Feynman parameters representation. We first disentangle overlapping singularities using sector decomposition. Threshold singularities are treated with an…

A method is developed whereby spinor helicity techniques can be used to simplify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear.…

We calculate a class of one-loop six-point amplitudes in the Yukawa model. The construction of multi-particle amplitudes is done in the string inspired formalism and compared to the Feynman diagrammatic approach. We show that there exists a…

Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental…

In this article, we explore the structure of IR singularity of Feynman diagrams at one loop via power counting in loop momentum. The emphasis is on many known results which follow from this simple analysis.

In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…

In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and discuss introduce their…

We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules,…

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation…