Related papers: Asymmetric particle-antiparticle Dirac equation: f…
The basic principles of generalization of the group theoretical approach to the relativistic wave equations on curved spaces are examined. The general method of the determination of wave equations from the known symmetry group of a…
We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…
We derive a semiclassical equation of motion for a `composite' quark in strongly-coupled large-N_c N=4 super-Yang-Mills, making use of the AdS/CFT correspondence. The resulting non-linear equation incorporates radiation damping, and reduces…
The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4,R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a…
A systematic approach is developed in order to obtain spherically symmetric midisuperspace models that accept holonomy modifications in the presence of matter fields with local degrees of freedom. In particular, starting from the most…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation…
Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…
A new method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomic-like Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are obtained…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
We consider the reflection of a Dirac plane wave on a perfectly reflecting plane described by chiral MIT boundary conditions and determine the rotation of the spin in the reflected component of the wave. We solve the analogous problem for a…
The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing…
This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory.…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Based on the results of F. Wilf on the need to take into account the quantum-mechanical correspondence rules in the Dirac equation for an electron, it was shown that the equation obtained by giving physical meaning to $\alpha$-Dirac…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
These notes provide two derivations of the Lorentz-Dirac equation. The first is patterned after Landau and Lifshitz and is based on the observation that the half-retarded minus half-advanced potential is entirely responsible for the…
A de Broglie-Bohm like model of Dirac equation, that leads to the correct Pauli equations for electrons and positrons in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum…
The present theory is closely related to Dirac's equation of the electron, but not to his magnetic monopole theory, except for his relation between electric and magnetic charge. The theory is based on the fact, that the massless Dirac…
A model in which a Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor…