Related papers: Existence of global-in-time solutions to a general…
Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…
The recent literature shows a renewed interest, with various independent approaches, in the classical theories for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
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…
We discuss the relation of the Kerr-Newman spinning particle to the Dirac electron and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the Kerr-Newman geometry. As a…
Maxwell and Dirac fields in Friedmann-Robertson-Walker spacetime is investigated using the Newman-Penrose method. The variables are all separable, with the angular dependence given by the spin-weighted spherical harmonics. All the radial…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
When the Dirac equation was first published in 1928, three solutions appeared immediately within the same year, each describing the most important problem in physics at that time: the hydrogen atom. These solutions lifted some of the…
Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…
In this paper we study a self-consistent Vlasov-Fokker-Planck equations which describes the longitudinal dynamics of an electron bunch in the storage ring of a synchrotron particle accelerator. We show existence and uniqueness of global…
A solution of the Dirac equation in a strong laser field presenting a nonspreading wave packet in the rest frame of the electron is derived. It consists of a generalization of the self-accelerating free electron wave packet [Kaminer et al.…
A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of…
In a recent paper Calogero and Alcantara derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the "one and one-half"…
Dirac's leaping insight that the normalized anti-commutator of the {\gamma}^{\mu} matrices must equal the timespace signature {\eta}^{\mu}{\nu} was decisive for the success of his equation. The {\gamma}^{\mu}-s are the same in all Lorentz…
We have studied the Generalised Brans-Dicke theory and obtained exact solutions of a(t),phi(t),and omega(t) for different epochs of the cosmic evolution .We discuss how inflation,decceleration,cosmic acceleration can result from this…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
Solutions of the Dirac equation for an electron in the Coulomb potential are obtained using operator invariants of the equation, namely the Dirac, Johnson-Lippmann and recently found new invariant. It is demonstrated that these operators…
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac…
A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…
The Wheeler-DeWitt (WdW) equation does not describe any explicit time evolution of the wave function, and somehow related to this issue, there is no natural way of defining an invariant inner product that provides a viable probability…
We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in…