Related papers: Loops in SU(2) and Factorization
We summarize the standard factorization theorems for hard processes in QCD, and describe their proofs.
Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…
We discuss the screening masses and residue factorisation of the SU(3) (2+1)D theory in the dimensional reduction formalism. The phase structure of the reduced model is also investigated.
The existence of triangular and unitriangular factorizations has been extensively studied for untwisted Chevalley groups, as well as for twisted Chevalley groups of types other than ${}^2A_{2n} \ (n \geq 1)$. However, the case of twisted…
In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…
The linear delta expansion is applied to a calculation of the SU(2) mass gap on the lattice. Our results compare favourably with the strong-coupling expansion and are in good agreement with recent Monte Carlo estimates.
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop…
We study the Mathieu Conjecture for $SU(2)$ using the matrix elements of its unitary irreducible representations. We state a conjecture for the particular case $SU(2)$ implying the Mathieu Conjecture for $SU(2)$.
We address the near-collinear expansion of multiparticle NMHV amplitudes, namely, the heptagon and octagons in the dual language of null polygonal super Wilson loops. In particular, we verify multiparticle factorization of charged pentagon…
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase…
We extend the class of factorization theorems for non-global observables from fixed angular constraints to cross sections defined in terms of sequential jet clustering. The associated hard and soft functions depend not only on the…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
A Code loop on a binary linear code that is doubly even with a factor set is shown to be a central loop, conjugacy closed loop, Burn loop and extra loop. General forms of the identities that define the factor set of a code are deduced.
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…
In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…
In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…
We introduce a streamlined method for evaluating in-in loop integrals using dimensional regularization for diagrams with an arbitrary number of external legs and vertices, which complements earlier work and facilitates the extraction of the…
We show an integrality of the quantum SU(2)-invariant associated with a non-trivial first cohomology class modulo two.