Related papers: Tachyonic Dirac Equation Revisited
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…
We show that in theories of generalised teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also…
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincar\'e gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian…
More then 35 approaches to the Dirac equation derivation are presented. The various physical principles and mathematical methods are used. A review of well-known and not enough known contributions to the problem is given, the unexpected and…
In the present paper we analyze the spectrum of quasinormal modes for massive scalar and Dirac fields, allowing for both tardyonic ($\mu^2 >0$) and tachyonic ($\mu^2 <0$) masses, in the expanding and rotating cosmological background. The…
It is known that one can formulate an action in teleparallel gravity which is equivalent to general relativity, up to a boundary term. In this geometry we have vanishing curvature, and non-vanishing torsion. The action is constructed by…
The Two-Body Dirac equations of constraint theory are of special interest not only in view of applications for phenomenological calculations of mesonic spectra but also because they avoid no-go theorems about relativistic interactions.…
Transformation equations for the kinetic energy of a tardyon are derived in the limits of classical and of special relativity theory. Two formulas are presented. In the first one the energy of the particle in one of the involved reference…
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\"{o}dinger--Pauli theory. We here…
It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
Motivated by a recent and several earlier measurement results of the neutrino velocity, we attempt to resolve the apparent discrepancies between them from the viewpoint of mass-energy relation in special relativity. It is argued that a…
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
General relativity dynamics can be derived from different actions -- which depart from the Einstein-Hilbert action in boundary terms -- and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory…
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…