Effects of nontrivial topology with Coulomb-types scalar and vector potential on relativistic quantum motions of scalar charged bosons

Abstract

In this paper, we study the relativistic quantum motions of spin-zero scalar bosons confined by the quantum flux field in the presence of Coulomb-type scalar potential in the background of a topologically nontrivial 4D space–time. Afterwards, we introduce a Coulomb-like vector potential through a minimal substitution in the wave equation and determine the eigenvalue solutions of the quantum system analytically. In fact, it is shown there that the nontrivial topology of the geometry, Coulomb-types scalar and vector potential, and the quantum flux field influence the energy profile and wave function of the scalar bosons and get them modified. Also, the gravitational analogue of the Aharonov–Bohm effect is observed because the energy eigenvalue depends on the geometric quantum phase.