Related papers: An introduction to spinors
In this paper, the recently-introduced ELKO and the well-known Dirac spinor fields will be compared; however, instead of comparing them under the point of view of their algebraic properties or their dynamical features, we will proceed by…
The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
The behavior of spin-1/2 particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization…
The aim of this work is to provide the contributors to journals or Hybrid numbers, akin to spinors, possess a broad range of applications in mathematical physics, geometry, and mathematics. In this study, these two significant topics were…
Spin of elementary particles is the only kinematic degree of freedom not having classical corre- spondence. It arises when seeking for the finite-dimensional representations of the Lorentz group, which is the only symmetry group of…
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…
We compare the way one of us got spinors out of fields, which are a priori antisymmetric tensor fields, to the Dirac-K\"ahler rewriting. Since using our Grassmann formulation is simple it may be useful in describing the Dirac-K\"ahler…
We employ the polar re-formulation of spinor fields to see in a new light their classification into regular and singular spinors, these last also called flag-dipoles, further splitting into the sub-classes of dipoles and flagpoles: in…
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…
The use of Slater-type spinor orbitals in algebraic solution of the Dirac equation is investigated. The one- and two-center integrals constitute the matrix elements arising in generalized eigenvalue equation for one-electron atoms and…
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…
We show that the Dirac equation for real spinors can be naturally decomposed into a system of two first-order relativistic wave equations. The decomposition separates in a transparent way the real and imaginary parts of the Dirac equation…
(Talk presented at the 7th Marcel Grossmann Meeting on General Relativity, Stanford, CA, July 24-30, 1994) We study the semi-classical limit of the solution of the Dirac equation in a background electromagnetic/gravitational plane wave. We…
Coupling spinor fields to the gravitational field, in the setting of general relativity, is standardly done via the introduction of a vierbein field and the (associated minimal) spin connection field. This makes three types of indices…
Some aspects of Dirac spinors are resumed and studied in order to interpret mathematically the P and T operations in a gravitational field.
We show that Dirac 4-spinors admit an entirely equivalent formulation in terms of 2-spinors defined over the split-quaternions. In this formalism, a Lorentz transformation is represented as a $2 \times 2$ unitary matrix over the…
For relativistic particles with spin 1/2, which are described by the Dirac equation, a semiclassical trace formula is introduced that incorporates expectation values of observables in eigenstates of the Dirac-Hamiltonian. Furthermore, the…
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to…
We define and study, under suitable assumptions, the fundamental class, the index class and the rho class of a spin Dirac operator on the regular part of a spin stratified pseudomanifold. More singular structures, such as singular…