In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive , two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of ex...

The main idea of renormalization is to correct the original Lagrangian of a quantum field theory by an infinite series of counterterms, labelled by the Feynman graphs that encode the combinatorics of the perturbative expansion of the theory. These counterterms have the effect of cancelling the ultraviolet divergences. Thus, in the procedure of perturbative renormalization, one introduces a coun...

The main idea of renormalization is to correct the original Lagrangian of a quantum field theory by an infinite series of counterterms, labelled by the Feynman graphs that encode the combinatorics of the perturbative expansion of the theory. These counterterms have the effect of cancelling the ultraviolet divergences. Thus, in the procedure of perturbative renormalization, one introduces a coun...

This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D2kR4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide pow...

Details of recent developments of the Feynman diagram analyzer DIANA (DIagram ANAlyser) are presented. Apart from some discussion about QGRAF and new plotting features, we concentrate on a new sophisticated mechanism of momenta mapping. The C-program DIANA (DIagram ANAlyser) for the automatic Feynman diagram evaluation was first documented in [1] 1. Meanwhile there exists a growing series of ap...

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of ‘degroupoidification’: a systematic process that turns groupoids and spans into vector spaces and linear operators. Then we present two applications of groupoidification. The first is to Fe...

This thesis covers the topic of applying the method of Feynman diagram sampling to quantum field theories. The method uses a computer simulation to sample the diagrammatic space obtained in a series expansion. For running large physical simulations powerful computers are required. Therefore, two independent parts are supplied. The first part deals with the method of Feynman diagram sampling. Th...

We derive the simplest commutation relations of operator algebras associated to M2 branes and an M5 brane in \Omega Ω -deformed M-theory, which is a natural set-up for Twisted holography. Feynman diagram 1-loop computations twisted-holographic dual side reproduce same algebraic relations.

A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model. As a first step an algorithm, proposed by F. V. Tkachov and based on the so-called generalized Bernstein functional relation, is applied to one-loop multi-l...