相关论文: Two-loop vacuum diagrams and tensor decomposition

The lectures are a practical introduction to perturbative calculations in QED and QCD. I discuss methods of calculation of one- and two-loop diagrams in dimensional regularization, MSbar and on-shell renormalization schemes, decoupling of…

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…

Two-dimensional (2D) convolutional codes are a generalization of (1D) convolutional codes, which are very appropriate for transmission over an erasure channel. In this paper, we present a decoding algorithm for 2D convolutional codes over…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…

An analytical approach is applied to the calculation of some dimensionally-regulated two-loop vertex diagrams with essential on-shell singularities. Such diagrams are important for the evaluation of QED corrections to the muon decay, QCD…

The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…

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…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…

A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.

Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams arXiv:2206.09368. Using this method on the ADE series of Toda models, we computed the…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

We present results for two-loop diagrams with massive quarks in the eikonal approximation. Explicit expressions are given for the UV poles in dimensional regularization of several of the required integrals.

Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…

The scalar two-loop master diagram is revisited in the massive cases needed for the computation of boson and fermion propagators in QED and QCD. By means of the causal method it is possible in a straightforward manner to express the…

An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this…

We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…

Some practical applications of algebraic renormalization are discussed. In particular we consider the two-loop QCD corrections to the three-gauge-boson vertices involving photons, Z and W bosons. For this purpose also the corresponding…