Related papers: Spin(11,3), particles and octonions
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…
In this paper we show that the nontrivial fundamental group $\pi_1 SO(3) ={\Bbb Z}_2$ for the group SO(3) of global proper rotations of a four-dimensional Euclidian space (when a spin structure is introduced preliminarily in that space)…
Spinor-valued one-forms (Rarita-Schwinger fields) are normally used in the context of supergravity, where they describe spin 3/2 particles (gravitinos). Indeed, when decomposed into irreducible representations of the Lorentz group such a…
We consider a $A_{N-1}$ type of spin dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as…
The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic `building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved…
We investigate higher spin AdS$_{3}$ gravity with real split forms of complex A$_{N}$ B$_{N}$, C$_{N}$ and D$_{N}$ Lie algebras. This is done by linking $SO(1,2)$ spin multiplets with splitted root systems using Tits-Satake diagrams of real…
We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having $k$ rows, on a basis of the BRST--BFV approach suggested for…
Let $LG$ be the loop group of a compact, connected Lie group $G$. We show that the tangent bundle of any proper Hamiltonian $LG$-space $\mathcal{M}$ has a natural completion $\overline{T}\mathcal{M}$ to a strongly symplectic…
In the context of supersymmetric $SO(10)$ grand unified models, it is shown that the gauge symmetry breaking as well as a natural doublet--triplet splitting can be achieved with a minimal Higgs system consisting of a single adjoint and a…
General topologically invariant microscopical expressions for quantum numbers of particle-like solitons ("skyrmions") are derived for a class of (2+1)D models. Skyrmions are either half-integer spin fermions with odd electric charge or…
We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…
We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, achieved by multiplying one of the gamma matrices by the imaginary number, $i$. The reason for doing this is to…
The nature of the effective spin Hamiltonian and magnetic order in the honeycomb iridates is explored by considering a trigonal crystal field effect and spin-orbit coupling. Starting from a Hubbard model, an effective spin Hamiltonian is…
The spinor-helicity representations of massive and (partially-)massless particles in four dimensional (Anti-) de Sitter spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (aka "little…
In this letter we apply the methods of our previous paper hep-th/0108045 to noncommutative fermions. We show that the fermions form a spin-1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations…
We discuss toroidal orbifolds of the E8XE8 heterotic string, in which the free fermionic Higgs-matter splitting is implemented by a shift in the internal lattice coupled with the fermion numbers of the gauge degrees of freedom. We consider…
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As…
A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a non-local unitary transformation. On an open chain, this…
In this paper, we define a new spinor classification that encompasses the recently proposed spin-half bosons with mass dimension three-half. As it will be shown, these particles, which are governed by a first-order equation and consequently…
In this paper a description of the Hubbard model on the square lattice with nearest-neighbor transfer integral $t$, on-site repulsion $U$, and $N_a^2\gg 1$ sites consistent with its exact global $SO(3)\times SO(3)\times U(1)$ symmetry is…