Related papers: Generalized Dirac and Klein-Gordon equations for s…
A new class of exact solutions of the bound Dirac and bound Klein Gordon equations in non co propagating plane waves is found. The solutions are based on the physical principle of maintaining local gauge invariance in the Furry picture…
This paper generalizes the method of deducing Dirac's equation to constructing a family of equations that represent the $N$-th root of the basic Energy-Momentum relation for a free particle \cite{Dattoli1, Dattoli2, Dattoli3, Dattoli4}.…
Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute…
The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some…
We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein-Gordon, and Dirac equations. Our analyze includes two main subsections: ($i$) statistical functions for the…
The equations for various spin particles with oscillator-like interactions are discussed in this talk. Contents: 1. Comment on "The Klein-Gordon Oscillator"; 2. The Dirac oscillator in quaternion form; 3. The Dirac-Dowker oscillator; 4. The…
In this paper, we consider the Dirac-Coulomb equation for many-particles, to describe the interaction between electrons in the system having many electrons. The four-component wave function will expanding into a finite basis-set, using…
The worldline of a free electron is revealed by applying Dirac's velocity operator to its Dirac wave function whose space-time arguments are expressed in a proper time by a Lorentz transformation. This motion can be decomposed into two…
We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac…
The Dirac equation governs the behaviour of spin-1/2 particles. The equation's separability into decoupled radial and angular differential equations is a crucial step in analytical and numerical computations of quantities like eigenvalues,…
We present an approximate analytic solution of the Klein-Gordon equation in the presence of equal scalar and vector generalized deformed hyperbolic potential functions by means of parameteric generalization of the Nikiforov-Uvarov method.…
General relativity is derived from an action which is quadratic in the covariant derivative of certain spinor one-form gravitational potentials. Either a pair of 2-component spinor one-forms or a single Dirac spinor one-form can be…
The Wheeler-DeWitt equation for the Bianchi Class A cosmological models is expressed generally in terms of the second-order differential equation like the Klein-Gordon equation. To obtain the positive-definite probability density, a new…
We point out that the anticommutation properties of the Dirac matrices can be derived without squaring the Dirac hamiltonian, that is, without explicit reference to the Klein-Gordon equation. We only require the Dirac equation to admit two…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
The Schrodinger equation, Klein-Gordon equation (KGE), and Dirac equation are believed to be the fundamental equations of quantum mechanics. Schrodinger's equation has a defect in that there are no negative kinetic energy (NKE) solutions.…
After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown,…
Relying on the variational principle, it is proved that new contradictions emerge from an analysis of the Lagrangian density of the Klein-Gordon field: normalization problems arise and interaction with external electromagnetic fields cannot…
The concept of elementary particle rests on the idea that it is a physical system with no excited states, so that all possible states of the particle are just kinematical modifications of any one of them. In this way instead of describing…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…