Related papers: The Pauli equation in scale relativity
After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented…
We deal with the ``nonrelativistic limit'', i.e. the limit c to infinity, where c is the speed of light, of the nonlinear PDE system obtained by coupling the Dirac equation for a 4-spinor to the Maxwell equations for the self-consistent…
A neo-classical relativistic mechanics theory is presented where the spin of an electron is a natural part of its space-time path as a point particle. The fourth-order equation of motion corresponds to the same Lagrangian function in proper…
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…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
It was pointed out in a previous paper that although neither the Klein-Gordon equation nor the Dirac Hamiltonian produces sound solitary free-particle relativistic quantum mechanics, the natural square-root relativistic Hamiltonian for a…
In this paper, we obtained the three-dimensional Pauli equation for a spin-1/2 particle in the presence of an electromagnetic field in noncommutative phase-space, as well the corresponding deformed continuity equation, where the cases of a…
Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…
We derive an equivalent traveling wave form description for Dirac field. In the non-relativistic limit, such form can reduce to inverse-Galilean transformed Schrodinger-type equation. We find that, the resulting two-component…
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…
Modified dispersion relations (MDRs) and noncommutative geometries are phenomenological models of Planck-scale corrections to relativistic kinematics, motivated by several approaches to quantum gravity. High-energy astrophysical…
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…
Newtonian gravity arises as the nonrelativistic, static, weak-field limit of some Lorentzian spacetime geometry solving the generally covariant Einstein equations for a given matter field configuration. Spacetime geometry has a local…
A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit existence of the non-relativistic limit in the covariant Dirac equation. Procedure…
In this paper, we give a rigorous derivation of Einstein's geodesic hypothesis in general relativity. We use scaling stable solitons for nonlinear wave equations to approximate the test particle. Given a vacuum spacetime $([0,…
We propose that the four-velocity of a Dirac particle is related to its relativistic wave function by $u^i=\bar{\psi}\gamma^i\psi/\bar{\psi}\psi$. This relativistic wave$-$particle duality relation is demonstrated for a free particle…
We discuss the theoretical basis for the search of the possible experimental manifestations of the torsion field at low energies. First, the quantum field theory in an external gravitational field with torsion is reviewed. The…
The Pauli equations describing electron (hole) dynamics in 2D Dirac-like intrinsic semiconductors in external (impurity) scalar potential and for inhomogeneous lattice distortions are obtained within second quantization approach. We show…
This article is the second in a series of two presenting the Scale Relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. Here, we show Schroedinger's equation to be a reformulation of Newton's…
Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to…