Related papers: Geometrization of quantum formalism
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…
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…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
The Dirac equation is used to provide a relativistic calculation of the binding energy of a hydrogen-like atom confined within a penetrable spherical barrier. We take the potential to be Coulombic within the barrier and constant outside the…
A new synthesis of the principles of relativity and quantum mechanics is developed by replacing the Poincar\'e group for the de Sitter one. The new relativistic quantum mechanics is an indefinite mass theory which is reduced to the standard…
We investigate the influence of gravitational waves on a freely falling hydrogen atom by analyzing the dynamics of the bound electron described by the Dirac equation in the curved spacetime of a gravitational wave. From this, we derive the…
Here is constructed a heuristic, first-order differential equation for the electromagnetic field in the vacuum, based on a phenomenological \textsl{ad hoc} argument. The formal similarity between this \textsl{ad hoc} wave equation and the…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar \omega $ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
It is shown that V.A.Fock's theory of hydrogen atom gives an example of the non-relativistic Snyder-like Quantum Geometry (QG).
Within the framework of classical field theory, the connection between the Dirac field as the field of matter and the spacetime metric is discussed. Polarization structure of the Dirac field is shown to be rich enough to determine the…
A number of physical processes occurring in a flat one-dimensional graphene structure under the action of strong time-dependent electric fields are considered. It is assumed that the Dirac model can be applied to the graphene as a subsystem…
This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The…
By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory…
In Dirac's canonical quantization theory on systems with second-class constraints, the commutators between the position, momentum and Hamiltonian form a set of algebraic relations that are fundamental in construction of both the quantum…
The extended algebra of the free electromagnetic fields, including infrared singular fields, and the almost radial gauge, both introduced earlier, are postulated for the construction of the quantum electrodynamics in a Hilbert space (no…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…