Related papers: Tensor Integrals for Two Loop Standard Model Calcu…
We report on tensor reduction of five point integrals needed for the evaluation of loop-by-loop corrections to Bhabha scattering. As an example we demonstrate the calculation of the rank two tensor integral with cancellation of the spurious…
We present a new method for evaluating tensor integrals in the large-scale structure. Decomposing a $\Lambda$CDM-like universe into a finite sum of scaling universes using the FFTLog, we can recast loop integrals for biased tracers in the…
A general method for reducing tensor form factors, that appear in one-loop calculations in dimensional regularization, to scalar integrals is presented. The method is an extension of the reduction scheme introduced by Passarino and Veltman…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order conservation law of a scalar partial differential equation, but integrable systems…
Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…
We perform analytical reductions of one-loop tensor integrals with 5 and 6 legs to scalar master integrals. They are based on the use of recurrence relations connecting integrals in different space-time dimensions. The reductions are…
In this paper, I present a technique to simplify the tensorial reduction of one-loop integrals with arbitrary internal masses, but at least two massless external legs. By applying the method to rank l tensor integrals, one ends up with at…
The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
The method introduced in a previous paper to simplify the tensorial reduction in multi-leg loop calculations is extended to generic one-loop integrals, with arbitrary internal masses and external momenta.
We present a method for reducing general two-loop self-energies to standard scalar integrals in massive gauge theories with special emphasis on the electroweak Standard Model. It includes the tensor integral reduction for all two-loop…
We introduce $\mathsf{LEM}$, a type-assignment system for the linear $ \lambda $-calculus that extends second-order $\mathsf{IMLL}_2$, i.e., intuitionistic multiplicative Linear Logic, by means of logical rules that weaken and contract…
We present a novel approach for the numerical solution of problems of diffraction by open arcs in two dimensional space. Our methodology relies on composition of {\em weighted versions} of the classical integral operators associated with…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…
The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…
The problem of simplifying tensor expressions is addressed in two parts. The first part presents an algorithm designed to put tensor expressions into a canonical form, taking into account the symmetries with respect to index permutations…
We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…