Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time: I. Klein–Gordon oscillator

Abstract

We analyse the Klein–Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator

“…4 of Paper 1, Ref. [12], which shows how differently the non-commutative parameter Ω 3 impacts the DKP-like oscillator in comparison with the KG oscillator. In fact, by comparing the y-axis values of the plot in Fig.…”

“…Our goal is to compare the results herein with those obtained in Ref. [12], hence referred to as Part 1.…”

“…Indeed, as we did in Ref. [12], the standard oscillator prescription consists of taking the non-minimal coupling…”

The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

“…Now, from a nonrelativistic point of view, the combination of these two effects has already been applied in the study of quantum dots [138], scattering [139], bound states for neutral particles with AMM and electric dipole moment [140], and in the QHE [141]. Recently, the Dirac, Klein-Gordon, and DKP-like oscillators have been studied under the influence of the noncommutativity and noninertial effects in a cosmic string spacetime [142][143][144]. However, in all these works, only the purely static case of the CS was considered, i.e., its intrinsic spin angular momentum or simply its angular momentum was not taken into account.…”

“…Be-sides, in Refs. [142][143][144] the NC of the positions was also not taken into account. Therefore, for a more general description, in our work, we consider a CS with an angular momentum non-null and also the NC of the positions, respectively.…”