Duffin–Kemmer–Petiau oscillator in topologically charged Ellis–Bronnikov-type wormhole

We explore relativistic quantum dynamics of spin-$0$ bosonic fields governed by the Duffin–Kemmer–Petiau (DKP) equation within the context of a topologically charged Ellis–Bronnikov-type wormhole. We derive the radial equation for the quantum systems described by the DKP equation on this wormhole background, ultimately arriving at the confluent Heun differential equation form. As a specific case, we present the ground energy level and the corresponding wave function of this quantum system. Furthermore, we extend our investigation to the DKP oscillator in the considered wormhole background, employing a similar methodology to deduce the ground state energy levels and wave function of the quantum oscillator field. Additionally, we introduce a zeroth component of the electromagnetic four-vector potential and examine the DKP oscillator by considering two types of potential on this wormhole background. Our findings highlight the influence of the wormhole throat radius and the topological charge of the geometry. Moreover, we observe that different external potentials also impact the energy levels of this relativistic quantum system.