相关论文: Spinors and Octonions

It is shown that models of elementary particles in classical general relativity (geons) will naturally have the transformation properties of a spinor if the spacetime manifold is not time orientable. From a purely pragmatic interpretation…

Fermion fields on an M-theory five-brane carry a representation of the double cover of the structure group of the normal bundle. It is shown that, on an arbitrary oriented Lorentzian six-manifold, there is always an Sp(2) twist that allows…

We briefly review the distinction between abstract groups and symmetry groups of objects, and discuss the question of which groups have appeared as the symmetry groups of physical objects. To our knowledge, the quaternion group (a beautiful…

The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the…

The notion of the spin is shown to have two constituents, as exemplified by the spin of the electron. The first one is related to the form of the wave equation and determines the fermion or boson particle type. This implies the spin taking…

One of the main goals of these notes is to explain how rotations in reals^n are induced by the action of a certain group, Spin(n), on reals^n, in a way that generalizes the action of the unit complex numbers, U(1), on reals^2, and the…

Set theory brought revolution to philosophy of mathematics and it can bring revolution to philosophy of physics too. All that stands in the way is the intuition that sets of physical objects cannot themselves be physical objects, which…

The formalism of quantum field theory in operator form, based on the anti self-adjoint operators of the imaginary coordinate and momentum and the self-adjoint operators of the real coordinate, momentum, energy and time, is used in…

We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…

We use the methods of group theory to reduce the equations of motion of two spin systems in (2+1) dimensions to sets of coupled ordinary differential equations. We present solutions of some classes of these sets and discuss their physical…

Using complexified quaternions, an intriguing link between generators of two different and surprisingly commuting four-dimensional representations of the SU(2)xU(1) Lie group, and generators of two four-dimensional spin 1/2 representations…

These are the notes for a course on representations of quivers for second year students in Paderborn in summer 2007. My aim was to provide a basic introduction without using any advanced methods. It turns out that a good knowledge of linear…

In this paper, by using bi-periodic Fibonacci numbers, we introduce the bi-periodic Fibonacci octonions. After that, we derive the generating function of these octonions as well as investigated some properties over them. Also, as another…

An overview of the history of projective representations (= spin representations) of groups, preceded by the prehistory of studies on the theory of quaternion due to Rodrigues and Hamilton. Beginning with Schur, we cover many mathematicians…

The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. The suggested formalism allows to address some subtle issues which…

Intermediate spin, which occurs in the theory of anyons, can also be exhibited by mesoscopic magnetic particles. The necessary broken time reversal symmetry is due to a suitably directed magnetic field. As a function of this field a system…

Some facts of the theory of the Lorentz group are specified for looking at the problems of light polarization optics in the frames of vector Stokes-Mueller and spinor Jones formalism. In view of great differences between properties of…

This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split…

We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…