Related papers: Modern techniques of multiloop calculations
This article is the first of a series of three presenting an alternative method to compute the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following 't Hooft and…
In recent years, commercial HTS superconductors have gained an increasing interest for their use in applications involving large-scale superconductor systems. These systems are typically made from hundreds to thousands of turns of…
The author's presentation of multilevel Monte Carlo path simulation at the MCQMC 2006 conference stimulated a lot of research into multilevel Monte Carlo methods. This paper reviews the progress since then, emphasising the simplicity,…
We review the recent developments of the Loop-Tree Duality method, focussing our discussion on the first numerical implementation and its use in the direct numerical computation of multi-leg Feynman integrals. Non-trivial examples are…
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 report on the new functionality of the open-source Mathematica package FeynCalc relevant for multiloop calculations. In particular, we focus on such tasks as topology identification by means of the Pak algorithm, search for equivalent…
Loop Tree Duality (LTD) offers a promising avenue to numerically integrate multi-loop integrals directly in momentum space. It is well-established at one loop, but there have been only sparse numerical results at two loops. We provide a…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
Recent progress in the calculation of multi-loop, multi-scale diagrams is reviewed. Expansion techniques combined with new developments in Computer algebra allow to evaluate the R ratio for massive quarks up to order $\alpha_s^2$ and,…
We review recent advances towards the computation of string couplings. Duality symmetry, mirror symmetry, Picard-Fuchs equations, etc. are some of the tools.
A brief overview of some recent publications related to the evaluation of two-loop Feynman diagrams is given. (Talk given at the International Symposium on Radiative Corrections CRAD96, Cracow, Poland, 1--5 August 1996)
We present a semi-numerical method to compute one-loop corrections to processes involving many particles. We treat in detail cases with up to five external legs and massless internal propagators, although the method is more general.
By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…
Current and future colliders will provide high precision experimental data. In order to use the high experimental precision it has to be matched with theoretical predictions at the same level of accuracy or better. This involves the…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
Physics of dielectric mixtures are presented to stimulate discussion and to provide information on the recent advances in this topic.