Related papers: Extensions in FormCalc 5.3
New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.
A C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented.
SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present…
Diagrammatic approaches to perturbation theory transformed the practicability of calculations in particle physics. In the case of extended theories of gravity, however, obtaining the relevant diagrammatic rules is non-trivial: we must…
We present a review of the Bielefeld-Dubna activities on the multiloop calculations. In the first part a C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented, in the second part various…
We present an alternative technique for evaluating multiloop Feynman diagrams, using the integration by fractional expansion method. Here we consider generic diagrams that contain propagators with radiative corrections which topologically…
Co-operation of the Feynman DIagram ANAlyzer (DIANA) with the underlying operational system (UNIX) is presented. We discuss operators to run external commands and a recent development of parallel processing facilities and an extension in…
We present FaRe, a package for Mathematica that implements the decomposition of a generic tensor Feynman integral, with arbitrary loop number, into scalar integrals in higher dimension. In order for FaRe to work, the package FeynCalc is…
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…
Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B.…
New developments concerning the extension of the Feynman diagram analyzer DIANA are presented. We discuss new graphics facilities, different approaches to automation of momenta distribution and parallel processing facilities. Furthermore…
We present a new FORM program for analytically evaluating four-loop massless propagator-type Feynman integrals in an efficient way. Our program Forcer implements parametric reductions of the aforementioned class of Feynman integrals into a…
We show that the calculation of L-loop Feynman integrals in D dimensions can be reduced to a series of matrix multiplications in D times L dimensions. This gives rise to a new type of expansions for the critical exponents in three…
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and $\varphi^k$ theories. Using dedicated graph theoretic tools…
We report on the development of tools to calculate loop integrals and amplitudes beyond one loop. In particular, we review new features of the program SecDec which can be used for the numerical evaluation of parametric integrals like…
A brief review of recent results on asymptotic expansions of Feynman integrals on the mass shell in momenta and masses and their application to 2-loop calculations is presented.
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
We present an extension of the program golem95C for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes, which supports tensor ranks exceeding the number of propagators. This…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
Understanding astrophysical and cosmological processes can be challenging due to their complexity and lack of intuitive analogies. To address this, we present \texttt{AstronomyCalc}, a Python package specifically designed to aid…