Using the hard-thermal-loop (HTL) resummation in real-time formalism, we study next-to-leading order (NLO) quark self-energy and corresponding NLO dispersion laws. In NLO, have replaced all propagators vertices with HTL-effective ones usual diagram. Additionally, a four-point vertex diagram also contributes to self-energy. We calculate separately. those, express terms of three- functions. Feynm...

We describe the implementation of the MSSM in the diagram generator FeynArts and the calculational tool FormCalc. This extension allows to perform loop calculations of MSSM processes almost fully automatically. The actual implementation has two aspects: The MSSM Feynman rules are specified in a new model file for FeynArts. The computation of the parameters in the MSSM Lagrangian from the input ...

This article reports an automated approach to the evaluation of higher-order terms of QED perturbation to anomalous magnetic moments of charged leptons by numerical means. We apply this approach to tenth-order correction due to a particular subcollection of Feynman diagrams, which have no virtual lepton loops. This set of diagrams is distinctive in that it grows factorially in number as the ord...

The propagator of a virtual φ-field with emission of n on-mass-shell particles all being exactly at rest is calculated at the tree-level in λφ 4 theory by directly solving recursion equations for the sum of Feynman graphs. It is shown that the generating function for these propagators is equivalent to a Fourier transform of the recently found Green's function within the background-field techniq...

An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar\'e is presented. These quantities emerge in analytic single multi--scale Feynman diagram calculations. To compactify representations, one wishes to apply general properties these computer-algebraic implementations. We provide the reduction basis expansions, continuation numer...

Since the Connes–Kreimer Hopf algebra was proposed, revisiting present quantum field theory has become meaningful and important from algebraic points. In this paper, the Hopf algebra in the cutting rules is constructed. Its coproduct contains all necessary ingredients for the cutting equation crucial to proving the perturbative unitarity of the S-matrix. Its antipode is compatible with the caus...

This paper describes a package for calculations of expressions with Dirac matrixes. Advantages to existing similar packages are described. MatrixExp package is intended for simplification of complex expressions involving γ-matrixes, providing such tools as automatic Feynman parameterization, integration in d-dimensional space, sorting and grouping of results in a given order. Also, in compariso...

In this paper we show how to improve and extend the Integration by Fractional Expansion technique (IBFE) by applying it to certain families of scalar massive Feynman diagrams. The strategy is based on combining this method together with the Integration by Parts technique (IBP). In particular, we want to calculate certain Feynman diagrams which have a triangle loop as a subgraph. The main idea i...

We argue that isotropization and, consequently, thermalization of the system of gluons and quarks produced in an ultrarelativistic heavy ion collision does not follow from Feynman diagram analysis to any order in the coupling constant. We conclude that the apparent thermalization of quarks and gluons, leading to success of perfect fluid hydrodynamics in describing heavy ion collisions at RHIC, ...

Feynman diagrams are the best tool we have to study perturbative quantum field theory. For this very reason the development of any new technique which allows us to compute Feynman integrals is welcome. By the middle of the 80’s, Halliday and Ricotta suggested the possibility of using negative dimensional integrals to tackle the problem. The aim of this work is to revisit the technique as such a...