相关论文: Spinors and Octonions

Let G be a connected reductive group over a field of characteristic zero, and consider an orthogonal representation of G. We give a simple criterion for whether the representation lifts to the spin group, in terms of the highest weights of…

In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two quaternionic components and the spin group is…

The paper aims to apply the algebra of octonions to explore the contributions of external derivative of electric moments and so forth on the induced electric currents, revealing a few major influencing factors relevant to the direct and…

This article aims at giving a general presentation of spintronics, an important field of research developing today along many new directions in physics of condensed matter. We tried to present simply the physical phenomena involved in…

A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are…

While general relativity provides a complete geometric theory of gravity, it fails to explain the other three forces of nature, i.e., electromagnetism and weak and strong interactions. We require the quantum field theory (QFT) to explain…

The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…

We emphasize that the group-theoretical considerations leading to SO(10) unification of electro-weak and strong matter field components naturally extend to space-time components, providing a truly unified description of all generation…

For any manifold M, the direct sum TM \oplus T*M carries a natural inner product given by the pairing of vectors and covectors. Differential forms on M may be viewed as spinors for the corresponding Clifford bundle, and in particular there…

A question is addressed pertinent to models of fundamental fermions in a world of high dimensions. Tex extra compactified dimensions are needed to accommodate quarks and leptons of each generation in a single spinor space carrying a…

We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems…

We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…

It is natural to study octonion Hilbert spaces as the recently swift development of the theory of quaternion Hilbert spaces. In order to do this, it is important to study first its algebraic structure, namely, octonion modules. In this…

In condensed matter theory many invaluable models rely on the possibility of subsuming fundamental particle interactions in constitutive relations for macroscopic fields in near equilibrium assemblies of particles. Should one wish to…

The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the…

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to…

The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by…

In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

There are two well-known ways of describing elements of the rotation group SO$(m)$. First, according to the Cartan-Dieudonn\'e theorem, every rotation matrix can be written as an even number of reflections. And second, they can also be…