Related papers: Linear and angular momentum spaces for Majorana sp…

I describe how the states of a discrete automata with p sites, each of which may be off or on, can be represented as Majorana spinors associated to a spacetime with signature (p,p). Some ideas about the quantization of such systems are…

The minimally extended standard model of particle physics contains three right handed or sterile neutrinos, coupled to the active ones by a Dirac mass matrix and mutually by a Majorana mass matrix. In the pseudo-Dirac case, the Majorana…

There are gauge-transformation operators applicable to massless spin-1/2 particles within the little-group framework of internal space-time symmetries of massive and massless particles. It is shown that two of the $SL(2,c)$ spinors are…

The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero…

We present a new analysis of the connection between the classical conservation theorems and the role played by the Dirac matrices in order to obtain a four spinor version of the Dirac equation for the two electrons bound problem. The…

We study the issue of description of spinning particle dynamics by means of recently proposed world sheet concept. A model of irreducible spinning particle in the $3d$ Minkowski space with two gauge symmetries is considered. The classical…

Lorentz transformations of spin density matrices for a particle with positive mass and spin 1/2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum.…

We present a Lagrangian formulation for 4d integer-spin relativistic fields in the 5d space spanned by two conjugate Weyl spinors and a Lorentz-invariant proper-time coordinate. We construct a manifestly Poincare-invariant free classical…

There are constructed exact solutions of the quantum-mechanical equation for a spin S=1 particle in 2-dimensional Riemannian space of constant positive curvature, spherical plane, in presence of an external magnetic field, analogue of the…

We consider the bosonic fields which describe a particle which may exist in states with spins one and zero with different masses. All the linearly independent solutions of the equation for a free particle are obtained in the form of the…

A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over the hyperbolic number system. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the…

The nonlinearity of the conformal group is an essential factor that ruins the global conformal invariance for interacting material fields. In this paper we attempt to track such nonlinearity from spacetime transformations to spinor…

It is an easily deduced fact that any four-component spin 1/2 state for a massive particle is a linear combination of pairs of two-component simultaneous rotation eigenstates, where `simultaneous' means the eigenspinors of a given pair…

This paper explores the relativistic behavior of spin--half particles possessing an Electric Dipole Moment (EDM) in a curved spacetime background induced by a spiral dislocation. A thorough review of the mathematical formulation of the…

The main purpose of this work is to show that massless Dirac equation formulated for non-interacting Majorana-Weyl spinors in higher dimensions, particularly in D=1+9 and D=5+5, can lead to an interpretation of massive Majorana and Dirac…

We demonstrate that a quantum field theory (QFT) in general two-dimensional curved spacetimes can be realized by a system of quantum spins or qubits. We consider a spin-1/2 model on a one-dimensional ring with spatially and temporally…

The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group;…

The paper analyzes time propagation of Dirac observables - using Heisenberg representation - in the light of various pseudodifferential operator algebras (cf. [Co3], [Co15], [Co16]). Our theory gives (i) a mechanical angular momentum (the…

We present a novel scheme where Dirac neutrinos are realized even if lepton number violating Majorana mass terms are present. The setup is the Randall-Sundrum framework with bulk right handed neutrinos. Bulk mass terms of both Majorana and…

In "Part I: Vector Analysis of Spinors", the author studied the geometry of two component spinors as points on the Riemann sphere in the geometric algebra of three dimensional Euclidean space. Here, these ideas are generalized to apply to…