Related papers: Algebraic decomposition of the electromagnetic con…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
After reviewing the construction of metric from premetric electrodynamics with empirical improvement of accuracy in the skewonless case, we explore the role of skewons in the construction of spacetime metric in the full premetric…
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
We present gravitoelectromagnetism and other decompositions of the Riemann tensor from the differential-geometrical point of view.
We present an algebraic approach to the internal structure of baryons in terms of three constituents. We investigate a collective model in which the nucleon is regarded as a rotating and vibrating oblate top with a prescribed distribution…
We suggest a simple phenomenological parametrization for all three deuteron electromagnetic form factors, and show that a good fit on the available data, with a minimal number of parameters, can be obtained. The present description of the…
New results about the electromagnetic form factors of the nucleon are obtained with a semirelativistic version of the hypercentral constituent quark model (hCQM) and a relativistic current. The complex structure of the constituent quarks is…
We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
The problem of unification of electro-magnetism and gravitation in four dimensions; some new ideas involving torsion. A metric consisting of a combination of symmetric and anti-symmetric parts is postulated and, in the framework of general…
The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way…
Electrodynamics with a local and linear constitutive law is used as a framework for models violating Lorentz covariance. The constitutive tensor of such a construction is irreducibly decomposed into three independent pieces. The principal…
In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of…
A phenomenological Lagrangian approach is employed to study the electromagnetic properties of deuteron. The deuteron is regarded as a loosely bound state of a proton and a neutron. The deuteron electromagnetic form factors are expressed in…
Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its…
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 reanalyze the world data on the electromagnetic form factors of the nucleon. The calculations are performed in the framework of an algebraic model of the nucleon combined with vector meson dominance.
We study the decomposition of central simple algebras of exponent 2 into tensor products of quaternion algebras. We consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension. Let $B$…
In the framework of generally covariant (pre-metric) electrodynamics (``charge & flux electrodynamics''), the Maxwell equations can be formulated in terms of the electromagnetic excitation $H=({\cal D}, {\cal H})$ and the field strength…