Related papers: Electromagnetic Klein-Gordon and Dirac equations i…
It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic…
A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless…
Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by…
A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The corresponding adiabatic dynamical and geometrical…
Metric-affine gravity (GL(4) gauge theory) in 4-dimensions is coupled to a spacetime Dirac source field using the isomorphisms of the Lie algebra gl(4) to the Clifford algebras Cl(3,1) and Cl(2,2). A simple transformation relates the…
There have been some long-standing puzzles related to the Coulomb solutions of the Klein-Gordon and Dirac equations, namely how to understand the physics underlying the weakly divergent near-the-origin behavior of the $S$-wave wave…
We establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…
This article presents the generalization of a zero spin hydrogen atom to a relativistic atomic model of hydrogen with dyons using the Klein--Gordon equation. The derivation of the Klein--Gordon equation for the particle of relative motion…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
The gravitational and electromagnetic fields of a moving charged spinning point particle are obtained in the Lorentz covariant form by transforming the Kerr--Newman solution in Boyer--Lindquist coordinates to the one in the coordinate…
On the basis of a general action principle, we revisit the scale invariant field equation using the co-tensor relations by Dirac (1973). This action principle also leads to an expression for the scale factor $\lambda$, which corresponds to…
We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers…
This article motivates and presents the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. It stems from the scale relativity proposal to extend the principle of relativity to…
The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
In the present article, using a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting…
We study a new approach to generally covariant quantum mechanics applied in the case of an FLRW cosmological background. For positive spatial curvature we find a discrete series of solutions of the Klein-Gordon equation that can reasonably…
In the standard Einstein-Cartan theory(EC), matter fields couple to gravitation field through the Minimal Coupling Procedure(MCP), yet leaving the theory an ambiguity: applying MCP to the action or to the equation of motion would lead to…