Relativistic quantum dynamics of spin-0 system of the DKP oscillator in a Gödel-type space-time

Abstract

In this article, we study the DKP equation for the oscillator in a Gödel-type space-time background. We derive the final form of this equation in a flat class of Gödel-type space-time and solve it analytically, and evaluate the eigenvalues and corresponding eigenfunctions, in detail.

Wave Fronts in a Causality-Violating Gödel-Type Metric

“…A particularly simple Type D metric has recently examined a member of a linear class of Gödel-type metrics [5]. Previously, relativistic quantum motion of spin-0 particle without interactions [6], linear confinement of a scalar particle subject to a scalar and vector potentials of Coulomb-types [7], Dirac equation [8], spin-0 system of DKP equation [9], and DKP oscillator [10] was investigated in this Type D metric.…”

“…With this solution for xðsÞ, we can solve for yðsÞ by simply substituting into Equation (10), with the result…”

“…This is trivial in the ẑ direction: p z = 0. From Equation (10) we see that for _ y = 0 at all s, we need to fix the value of p y :…”

Investigation of a Spin-0 Massive Charged Particle Subject to a Homogeneous Magnetic Field with Potentials in a Topologically Trivial Flat Class of Gödel-Type Space-Time

“…. Consider the following stationary space-time [50] (see [5,12,13,44,51]) in the Cartesian coordinates ðx 0 = t, x 1 = x, x 2 = y, x 3 = zÞ which is given by…”

“…Substituting the series solution (equation ( 19)) into equation (51), we obtain the following recurrence relation:…”