Related papers: Tensor reduction of loop integrals
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…
For a general third-order tensor $\mathcal{A}\in\mathbb{R}^{n\times n\times n}$ the paper studies two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. We develop a Jacobi-type algorithm…
Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators…
The aim of this paper is to present a mathematical framework for tensor PCA. The proposed approach is able to overcome the limitations of previous methods that extract a low dimensional subspace by iteratively solving an optimization…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…
This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D lattice-structured and periodic systems. The set of localized…
Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…
Using the Feynman parameter method, we have calculated in an elegant manner a set of one$-$loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and…
We present a generally applicable reduction formalism which makes it possible to express an arbitrary tensor and scalar one-loop Feynman integral, with N external lines and massless propagators, in terms of a basic set of eight fundamental…
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…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
The higher-order corrections become increasingly important with experiments reaching sub-percent level of uncertainty as they look for physics beyond the Standard Model. Our goal is to address the full set of two-loop electroweak…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction…