Related papers: Numerical evaluation of massive multi-loop integra…
The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set…
In this paper we discuss techniques, which lead to a significant improvement of the efficiency of the Monte Carlo integration, when one-loop QCD amplitudes are calculated numerically with the help of the subtraction method and contour…
We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…
The program ftint is introduced which numerically evaluates dimensionally regulated integrals as they occur in the perturbative approach to the gradient-flow formalism in quantum field theory. It relies on sector decomposition in order to…
We present a new method for the numerical evaluation of loop integrals which is based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…
We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package…
Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task.…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
These notes present some extensions of a formal method introduced in an earlier paper. The formal method is designed as a tool for program verification of numerical computation and forms the basis of the software package VPC. Included in…
This program can be used to simulate polarised nucleon - nucleon collisions at high energies. Spins of colliding particles are taken into account. The program allows to calculate cross sections for various processes.
This work explores an unexpected application of Implicit Computational Complexity (ICC) to parallelize loops in imperative programs. Thanks to a lightweight dependency analysis, our algorithm allows splitting a loop into multiple loops that…
We present OPITeR, a FORM program for the reduction of multi-loop tensor Feynman integrals. The program can handle tensors, including spinor indices, with rank of up to 20 and can deal with up to 8 independent external momenta. The…
Numerical reconstruction techniques are widely employed in the calculation of multi-loop scattering amplitudes. In recent years, it has been observed that the rational functions in multi-loop calculations greatly simplify under partial…
This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…
We describe an integration of program synthesis into Uclid5, a formal modelling and verification tool. To the best of our knowledge, the new version of Uclid5 is the only tool that supports program synthesis with bounded model checking,…
The program package GoSam is presented which aims at the automated calculation of one-loop amplitudes for multi-particle processes. The amplitudes are generated in terms of Feynman diagrams and can be reduced using either D-dimensional…