Related papers: A note on hidden classes in spinor classification

We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…

The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to…

We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…

The Heisenberg-Ising spin ladder is one of the few short-range models showing confinement of elementary excitations without the need of an external field, neither transverse nor longitudinal. This feature makes the model suitable for an…

Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.

We give new combinatorial formulas for decomposition of the tensor product of integrable highest weight modules over the classical Lie algebras of type $B, C, D$, and the branching decomposition of an integrable highest weight module with…

In this report, fundamental educational concepts of linear and non-linear equations and solutions of nonlinear equations from the book High-Temperature Superconductivity: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic…

This article contributes to the search for a notion of postural style, focusing on the issue of classifying subjects in terms of how they maintain posture. Longer term, the hope is to make it possible to determine on a case by case basis…

Linear spinor fields are a generalization of the Dirac field that have transparent cluster decomposability properties needed for classical correspondence of relativistic quantum systems. The algebra of these fields directly incorporate…

Convolutional neural networks typically encode an input image into a series of intermediate features with decreasing resolutions. While this structure is suited to classification tasks, it does not perform well for tasks requiring…

The hallmark of highly frustrated systems is the presence of many states close in energy to the ground state. Fluctuations between these states can preclude the emergence of any form of order and lead to the appearance of spin liquids. Even…

The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…

This paper concerns open-world classification, where the classifier not only needs to classify test examples into seen classes that have appeared in training but also reject examples from unseen or novel classes that have not appeared in…

We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus. For n>3 the classification…

We propose and apply simple machine learning approaches for recognition and classification of complex non-collinear magnetic structures in two-dimensional materials. The first approach is based on the implementation of the…

We investigate various types of squeezing in a collective su(2J+1) system consisting of spin-J particles (J>1/2). We show that the squeezing in the collective su(2J+1) system can be classified into unitary equivalence classes, each of which…

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong -- together with Majorana spinor fields -- to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5),…

In a previous work, we have constructed a reparametrization invariant worldsheet action from which one can derive the super-Poincare covariant pure spinor formalism for the superstring at the fully quantum level. The main idea was the…

We employ the polar re-formulation of spinor fields to see in a new light their classification into regular and singular spinors, these last also called flag-dipoles, further splitting into the sub-classes of dipoles and flagpoles: in…

We propose a model-independent framework to classify and study neutrino mass models and their phenomenology. The idea is to introduce one particle beyond the Standard Model which couples to leptons and carries lepton number together with an…