Fayçal Hammad

We investigate the curved-spacetime dynamics of charged spin- 1 2 particles minimally coupled to the electromagnetic field and propagating in superposed states of different masses. For that purpose, we make use of a Wentzel-Kramers-Brillouin approximation of the Dirac equation with a minimal coupling to the Maxwell field in curved spacetime. We obtain the spin dynamics as well as the deviation from geodesic motion of such particles. The problem of having the mass eigenstates experience different proper times, as opposed to the case of neutral particles, is here dealt with by first extracting the second-order differential equation obeyed by each superposition. This strategy proves to be not only powerful, but also very economical. Published by the American Physical Society 2024

The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within such a combination.

The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within a such a combination.

We study, using the Mathisson-Papapetrou-Dixon equations, the spin oscillation of neutrinos when the latter are coupled to the scalar field of screening models of dark energy. First, we derive the transition probability formula for a left-handed neutrino to become a right-handed neutrino within a general static and spherically symmetric metric. We then apply our general formula to neutrinos deflected around a central mass described by the Schwarzschild metric. Our results show that, contrary to what one might expect, the scalar field of chameleon-like and symmetron-like screening models would not show any effect on the spin oscillations of neutrinos. The origin of such an outcome is discussed.

We study, using the Mathisson-Papapetrou-Dixon equations, the spin oscillation of neutrinos when the latter are coupled to the scalar field of screening models of dark energy. First, we derive the transition probability formula for a left-handed neutrino to become a right-handed neutrino within a general static and spherically symmetric metric. We then apply our general formula to neutrinos deflected around a central mass described by the Schwarzschild metric. Our results show that, contrary to what one might expect, the scalar field of chameleonlike and symmetronlike screening models would not show any effect on the spin oscillations of neutrinos. The origin of such an outcome is discussed.

We recently studied neutrinos flavor oscillations in vacuum within conformal coupling models. In this paper, we extend that analysis by investigating neutrino flavor oscillations inside matter within a general conformal coupling scenario. We first derive the general formula for the flavor transition probability inside matter in arbitrary static and spherically symmetric spacetimes. The modified resonance formula of the MSW effect is derived and the corresponding adiabaticity parameter of the effect is extracted. An application of our results to the case of two-flavor neutrinos within the well-known chameleon and symmetron conformal coupling models is made.

We recently studied neutrinos flavor oscillations in vacuum within conformal coupling models. In this paper, we extend that analysis by investigating neutrino flavor oscillations inside matter within a general conformal coupling scenario. We first derive the general formula for the flavor transition probability inside matter in arbitrary static and spherically symmetric spacetimes. The modified resonance formula of the Mikheyev-Smirnov-Wolfenstein effect is derived and the corresponding adiabaticity parameter of the effect is extracted. An application of our results to the case of two-flavor neutrinos within the well-known chameleon and symmetron conformal coupling models is made.

In flat spacetime, the Dirac equation is the "square root" of the Klein-Gordon equation in the sense that by applying the square of the Dirac operator to the Dirac spinor, one recovers the Klein-Gordon equation duplicated for each component of the spinor. In the presence of gravity, applying the square of the curved-spacetime Dirac operator to the Dirac spinor does not yield the curved-spacetime Klein-Gordon equation, but yields, instead, the Schrödinger-Dirac covariant equation. First, we show that the latter equation gives rise to a generalization to spinors of the covariant Gross-Pitaevskii equation. Next, we show that while the Schrödinger-Dirac equation is not conformally invariant, there exists a generalization of the equation that is conformally invariant but which requires a different conformal transformation of the spinor than the one required by the Dirac equation. The new conformal factor acquired by the spinor is found to be a matrix-valued factor obeying a differential equation that involves the Fock-Ivanenko line element. The Schrödinger-Dirac equation coupled to the Maxwell field is then revisited and generalized to particles with higher electric and magnetic moments while respecting gauge symmetry. Finally, Lichnerowicz's vanishing theorem in the conformal frame is also discussed.