Related papers: On possible effects of the spinor structures in Qu…
It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar…
Because spatio-temporal tensors are associated with the Lorentz group, whereas spinors are associated with its covering group SL(2, C), one can associate with every tensor a spinor (but not vice versa). In particular, the (1,0)+(0,1)…
We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
This paper reviews some recent work on (s)pin structures and the Dirac operator on hypersurfaces (in particular, on spheres), on real projective spaces and quadrics. Two approaches to spinor fields on manifolds are compared. The action of…
An earlier scheme [arXiv:2404.03360], where torsion plays an essential part in a flat spacetime account of fermion spin, is extended to spacetimes with non-zero Riemann curvature. It is found that further essential features of the fermion,…
The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are…
Given Lorentz invariance in Minkowski spacetime, we investigate a common space of spin and spacetime. To obtain a finite spinor representation of the non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an indefinite…
This is a review of recent developments in hadron structure within the framework of Lattice QCD. The main focus is on recent achievements in the evaluation of nucleon quantities, such as the axial charge, electromagnetic form factors, the…
We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.
The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.
We introduce $\mathfrak{F}$-positive elements in planar algebras. We establish the Perron-Frobenius theorem for $\mathfrak{F}$-positive elements. We study the existence and uniqueness of the Perron-Frobenius eigenspace. When it is not…
The Einstein equations for an isotropic and homogeneous Friedmann--Robertson--Walker Universe in the presence of a quintessence scalar field are shown to be described in a unified way, formally identical to the dynamics of a relativistic…
Two topics are covered in this paper. In the first part the relation between quark mass matrices and observable quantities in gauge theories. In the second part neutrino masses and mixings in a seesaw framework.
We develop a spinor equation of the electromagnetic field, which is equivalent to the Maxwell equation and has a similar form as the Dirac equation. The spinor is the very conjugate momentum of the vector potential in the Lagrangian…
In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of so called generalized Killing spinors. We then discuss several applications, among…
Different bases for the spin-1 density matrix are discussed to clarify the connection between its components and observables measured in heavy-ion collisions. The theoretical advantage of using the adjoint representation for spin matrices…
A simple tight-binding theoretical model is proposed for spin dependent, current-in-plane transport in highly coherent spin valve structures under specularity conditions. Using quantum-mechanically coherent and spatially quantized Fermi…
Conformally compactified phase space is conceived as an automorphism space for the global action of the extended conformal group. Space time and momentum space appear then as conformally dual, that is conjugate with respect to conformal…
In this introductory review, we argue that a quantum structure of space-time naturally entails a higher-spin theory, to avoid significant Lorentz violation. A suitable framework is provided by Yang-Mills matrix models, which allow to…