Related papers: Simplifying 5-point tensor reduction
Consider a compact Riemannian manifold in dimension $n$ with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of $2$ tensors for $n\geq 3$ and the mixed ray transform of $2+2$…
In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…
The variational inclusion of spin-orbit coupling in self-consistent field (SCF) calculations requires a generalised two-component framework, which permits the single-determinant wave function to completely break spin symmetry. The…
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…
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…
Tensor distributions and their derivatives are described without assuming the presence of a metric. This provides a natural framework for discussing tensor distributions on manifolds with degenerate metrics, including in particular metrics…
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. In a recent paper [arXiv:0907.2994v1] we discussed how to…
The tensor product of $L$ copies of a single vector, such as $p_{i_1} ... p_{i_L}$, can be analyzed in terms of angular momentum. When $p_{i_1} ... p_{i_L}$ is decomposed into a sum of components $( p_{i_1} ... p_{i_L} )^L_\ell$, each…
Five-point functions and five-body wave functions play an important role in many areas of nuclear and particle physics, e.g., in 2 -> 3 scattering processes, in the five-gluon vertex, or in the study of pentaquarks. In this work we consider…
A theoretical formalism leading to elegant derivation of formulae for all spin observables is outlined for photo production of mesons with arbitrary spin parity $s^{\pi}$. The salient features of this formalism based on irreducible tensor…
Moment invariants are a powerful tool for the generation of rotation-invariant descriptors needed for many applications in pattern detection, classification, and machine learning. A set of invariants is optimal if it is complete,…
We give a gauge-invariant treatment of the angular momentum sum-rule for the proton in terms of matrix elements of three gauge-invariant, local composite operators. These matrix elements are decomposed into three independent form factors,…
The subrank of tensors is a measure of how much a tensor can be ''diagonalized''. This parameter was introduced by Strassen to study fast matrix multiplication algorithms in algebraic complexity theory and is closely related to many central…
In the present paper it is considered a class V of 3-dimensional Riemannian manifolds M with a metric g and two affinor tensors q and S. It is defined another metric \bar{g} in M. The local coordinates of all these tensors are circulant…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of…
We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring…
In this paper, we first introduce the invertibility of even-order tensors and the separable tensors, including separable symmetry tensors and separable anti-symmetry tensors, defined respectively as the sum and the algebraic sum of rank-1…
A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…