Related papers: Can Mathisson-Papapetrou equations give clue to so…
We consider extensions of the Dirac equation with mass terms m1+i*gamma5*m2 and i*m_1+gamma*m2. The corresponding Hamiltonians are Hermitian and pseudo-Hermitian ("gamma5 Hermitian"), respectively. The fundamental spinor solutions for all…
The Mashhoon rotation-spin coupling is studied by means of the parallelism description of general relativity. The relativistic rotational tetrad is exploited, which results in the Minkowski metric, and the torsion axial-vector and Dirac…
General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity,…
We consider generally-relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by…
In this paper, we study the relativistic and nonrelativistic Landau levels for Dirac fermions in the cosmic string spacetime in the context of rainbow gravity in $(3+1)$-dimensions, where we work with the curved Dirac equation with minimal…
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…
Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equations instead of the original metric $g$ emerges…
Deviation and precession effects of a bunch of spinning particles in the field of a weak gravitational plane wave are studied according to the Mathisson-Papapetrou-Dixon (MPD) model. Before the passage of the wave the particles are at rest…
Based on the results of F. Wilf on the need to take into account the quantum-mechanical correspondence rules in the Dirac equation for an electron, it was shown that the equation obtained by giving physical meaning to $\alpha$-Dirac…
We explore the possibility that the connection between spin and statistics in quantum physics is of dynamical origin. We suggest that the gravitational field could provide a fully local mechanism for the phase that arises when fermionic and…
The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should…
We constrain Horava-Lifshitz gravity using the results of OPERA and ICARUS neutrino speed experiments, which show that neutrinos are luminal particles, examining the fermion propagation in the earth's gravitational field. In particular,…
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear…
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The…
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…
This paper investigates a background charge one Skyrme field chirally coupled to light fermions on the 3-sphere. The Dirac equation for the system commutes with a generalised angular momentum or grand spin. It can be solved explicitly for a…
We derive the equations of state of Fermi gas by maximizing the Fermi-Dirac entropy in modified gravity in relativistic and non-relativistic case. It will be demonstrated that the microphysics must depend on a given theory of gravity in…
In this review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but $PT$ symmetric on microscopic ones. In particular we show that the…
We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying…
We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the…