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I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest…
We study the non-relativistic limit of Dirac equation for mixed neutrinos. We demonstrate that such a procedure inevitably leads to a redefinition of the inertial mass. This happens because, in contrast to the case when mixing is absent,…
Unbound interacting compact binaries emit gravitational radiation in a wide frequency range. Since short burst-like signals are expected in future detectors, such as LISA or advanced LIGO, it is interesting to study their energy spectrum…
We investigate potential quantum nonlinear corrections to Dirac's equation through its sub-leading effect on neutrino oscillation probabilities. Working in the plane-wave approximation and in the $\mu-\tau$ sector, we explore various…
We present analytic solutions of Maxwell equations in the internal and external background spacetime of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with…
We study a covariant classical model of neutral point particles with magnetic moment interacting with external electromagnetic fields. Classical dynamical equations which reproduce a correct behavior in the non-relativistic limit are…
Reporting about the formalism with the Dirac equation we describe the dynamics of chiral oscillations for a fermionic particle non-minimally coupling with an external magnetic field. For massive particles, the chirality and helicity quantum…
We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the…
A restriction was found in the mathematics of the Dirac equation for a free neutrino type of particle. The basic assumption here is the equivalence of the four variables of spacetime. A perspective is defined as a metric tensor format. We…
We present the basic prerequisites of electromagnetism in flat spacetime and provide the description of electromagnetism in terms of the Faraday tensor. We generalise electromagnetic theory to a general relativistic setting, introducing the…
We argue that the neutrino oscillation probabilities in matter are best understood by allowing the mixing angles and mass-squared differences in the standard parametrization to `run' with the matter effect parameter $a=2\sqrt{2}G_F N_e E$,…
This paper, devoted to the study of spectral pollution, contains both abstract results and applications to some self-adjoint operators with a gap in their essential spectrum occuring in Quantum Mechanics. First we consider Galerkin basis…
For Dirac particles interacting with external fields, we use the exact operator of the Foldy-Wouthuysen transformation obtained by Eriksen and rigorously derive a leading correction in the weak-field approximation to the known relativistic…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak…
A new method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomic-like Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are obtained…
The Dirac equation is considered with the recently proposed generalized gravitational interaction (Kepler or Coulomb), which includes post-Newtonian (relativistic) and quantum corrections to the classical potential. The general idea in…
We give a perturbation theory of neutrino oscillation in the Earth. The perturbation theory is valid for neutrinos with energy $E \gsim 0.5$ GeV. It is formulated using trajectory dependent average potential. Non-adiabatic contributions are…
In this study, we obtain the approximate analytical solutions of the radial Schrodinger equation for the New Generalized Morse-Like Potential in arbitrary dimensions by using the Nikiforov Uvarov Method. Energy eigenvalues and corresponding…
We discuss the relation of the Kerr-Newman spinning particle to the Dirac electron and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the Kerr-Newman geometry. As a…