Related papers: Dirac Theory as a Relativistic Flow
In previous papers we have shown how Schrodinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The…
In this work, the action of the relativistic electron is derived from the hydrodynamic formulation of the Dirac equation. In particular, in the hydrodynamic scenario, the four-velocity of the electron is regarded as an Eulerian field and…
The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity…
Classical relativistic field theory is applied to perfect and magneto-hydrodynamic flows. The fields for Hamilton's principle are shown to be the Lagrangian coordinates of the fluid elements, which are potentials for the matter current…
The formulation of a dynamical theory of General Relativity, including matter, is viewed as a problem of coupling Einstein's theory of pure gravity, formulated as an action principle, to an independently chosen and well defined field theory…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
A weakness which has previously seemed unavoidable in particle interpretations of quantum mechanics (such as in the de Broglie-Bohm model) is addressed here and a resolution proposed. The weakness in question is the lack of action and…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
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…
In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the…
The Lagrangian approach of Dirac is presented in a complete form. This suggests to identify the Schr\"{o}dinger equation as the Euler-Lagrange equation rather than the Hamiltonian operator equation.
The quantum hydrodynamic like equations as a function of two real sets of variables, the 4x4 action matrix and the 4 dimensional wave function modulus vector of the Dirac equation, are derived in the present work. The paper shows that in…
The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is…
Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that…
Method of the quantum hydrodynamics has been applied in quantum plasmas studies. As the first step in our consideration, derivation of classical semi-relativistic (i. e. described by the Darwin Lagrangian on microscopic level)…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the…