Global effects due to cosmic defects in Kaluza-Klein theory

Abstract

Using Kaluza-Klein theory we study the quantum mechanics of a scalar particle in the background of a magnetic cosmic string and in the background of a chiral cosmic string. We show that the wave functions, the phase shifts, and scattering amplitudes associated with the particle depend on the global features of those spacetimes. These dependences represent gravitational analogues of the well-known Aharonov-Bohm effect. In addition, we discuss the Landau levels in the presence of a cosmic string in the framework of Kaluza-Klein theory. ͓S0556-2821͑99͒03610-3͔

Harmonic oscillator in an elastic medium with a spiral dislocation

“…In particular, torsion effects related to the presence of topological defects are in the interests of studies of semiconductors [17][18][19][20]. Moreover, spacetimes with space-like disclinations and with space-like dislocations [4] have also been investigated as backgrounds of relativistic quantum systems [21][22][23][24][25][26][27]. On the hand, studies of an edge dislocation through differential geometry and its influence on quantum systems have not been widely explored.…”

Torsion effects on a relativistic position-dependent mass system

“…It is worth emphasizing that a spacetime with a space-like dislocation corresponds to a topological defect spacetime associated with the presence of torsion in the spacetime [38]. In quantum mechanics, the background defined by a spacetime with a space-like dislocation has been explored in studies of the Aharonov-Bohm effect for bound states [39], quantum scattering [40,41], harmonic oscillator [42], noninertial effects [43], Kaluza-Klein theory [44] and the Dirac oscillator [45].…”

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

“…Despite the Klein-Gordon oscillator is under the influence of a scalar potential, these two couplings yield different results, for instance, for the angular frequency ω 1, l and the relativistic energy level E 1, l associated with the ground state of the Klein-Gordon oscillator. It is worth mentioning that the influence of the Klein-Gordon oscillator and the Coulomb potential on a scalar particle can be of interest in studies of the quark-antiquark interaction [1], the Kaluza-Klein theory [69], the Casimir effect [70,71] and relativistic effects on condensed matters systems such as effects associated with linear topological defects in solids [72][73][74], the Aharonov-Bohm effect for bound states [75][76][77] and persistent currents [78,79].…”