Klein–Gordon oscillator in Kaluza–Klein theory

Abstract

In this contribution we study the Klein-Gordon oscillator on the curved background within the Kaluza-Klein theory. The problem of the interaction between particles coupled harmonically with topological defects in Kaluza-Klein theory is studied. We consider a series of topological defects, then we treat the Klein-Gordon oscillator coupled to this background, and we find the energy levels and corresponding eigenfunctions in these cases. We show that the energy levels depend on the global parameters characterizing these spacetimes. We also investigate a quantum particle described by the Klein-Gordon oscillator interacting with a cosmic dislocation in Som-Raychaudhuri spacetime in the presence of homogeneous magnetic field in a Kaluza-Klein theory. In this case, the energy spectrum is determined, and we observe that these energy levels represent themselves as the sum of the terms related with Aharonov-Bohm flux and of the parameter associated to the rotation of the spacetime.

Linear confinement of a scalar particle in a Gödel-type spacetime

“…This analogy also arises from the point of view of quantum mechanics, where the quantum dynamics of scalar and spinorial quantum particles in this spacetime is an analogue of the Landau levels, as observed in Refs. [8][9][10]16,17]. We shall discuss this point below.…”

“…They also compared with the Landau levels in the flat space. Recently, the scalar quantum particle has been investigated in the class of the Gödel solutions with a cosmic string passing through the spacetime [10].…”

“…In recent years, several authors have investigated the physical properties of a series of backgrounds with a cosmic string. For example, the Schwarzschild spacetime with a cosmic string [11,12], the Kerr spacetime with a cosmic string [13], Gödel-type spacetime with a cosmic string [10] and the cosmic string in AdS space [14]. Furthermore, it is worth mentioning the studies of a scalar quantum particle confined in two concentric thin shells in curved spacetime backgrounds with a cosmic string [15], the Klein-Gordon oscillator in a Som-Raychaudhuri spacetime with a cosmic dispiration [16], and fermions in a family of Gödel-type solutions with a cosmic string [17].…”

Relativistic quantum motion of spin-0 particles under the influence of noninertial effects in the cosmic string spacetime

“…In recent years, several studies have addressed the Klein-Gordon oscillator in quantum systems [49][50][51][52][53][54][55][56][57]. It has a formulation similar to the vector potential in the previous section, so to study its solutions we will use the following change in momentum operator:…”

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

“…It was proposed by Bruce and Minning [45] in analogy with the Dirac oscillator [49] and it has attracted interests in studies of noncommutative space [50,51], in noncommutative phase space [52], in Kaluza-Klein theories [53] and in PT -symmetric Hamiltonian [54]. The relativistic oscillator coupling proposed by Bruce and…”