Related papers: General Dynamics of Spinors
In this paper we present a detailed calculation of an Ansatz that allows to obtain spherically symmetric Einstein-Dirac configurations in $d$-dimensions. We show that this is possible by combining $2^{\lfloor \frac{d-2}{2} \rfloor}$ Dirac…
We consider the dynamics of Dirac particles moving in the curved spaces with one coordinate subjected to compactification and thus interpolating smoothly between three- and two-dimensional spaces. We use the model of compactification, which…
The local Lorentz group is introduced in flat space-time, where the resulting Dirac and Yang-Mills equations are found, and then generalized to curved space-time: if matter is neglected, the Lorentz connection is identified with the…
We have studied a relativistically covariant Stern-Gerlach (SG) experiment for a relativistic spin and a Dirac spin. We have obtained the relativistic spin in an arbitrary frame by using the classical spin dipole tensor, which gives the…
We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background. We solve the difficulties…
A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show…
We study the solutions to the Dirac equation for the massive spinor field in the universal covering space of two-dimensional anti-de Sitter space. For certain values of the mass parameter, we impose a suitable set of boundary conditions…
In frame of Dirac quantum field theory that describes electrons and positrons as elementary excitations of the spinor field, the generalized operator of the spin-orbit interaction is obtained using non-relativistic approximation in the…
We consider the most general axial torsion completion of gravity with electrodynamics for $\frac{1}{2}$-spin spinors in an $8$-dimensional representation of the Dirac matter field: this theory will allow to define antimatter as matter with…
We show that the coupling of a Dirac spinor field with the gravitational field in the teleparallel equivalent of general relativity is consistent. For an arbitrary SO(3,1) connection there are two possibilities for the coupling of the…
We discuss a new covariant scalar-tensor system aimed to realise Ho\v{r}ava proposal for a power-counting renormalizable theory of gravity, with the special feature of not propagating scalar degrees of freedom in an appropriate gauge. The…
After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
Motivated by supersymmetry methods in general relativity, we study four-dimensional Lorentzian space-times with a complex Dirac spinor field satisfying a Killing-spinor-like equation where the Killing constant is promoted to a complex…
This article studies a class of Dirac operators of the form $D_\varepsilon= D+\varepsilon^{-1}\mathcal A$, where $\mathcal A$ is a zeroth order perturbation vanishing on a subbundle. When $\mathcal A$ satisfies certain additional…
We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which…
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy-Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime…
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
The solitons and kinks of the generalized $sl(3, \IC)$ sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the {\sl tau} functions play an important role. The various properties are…