Relativistic quantum dynamics of vector bosons in an Aharonov-Bohm potential

The Aharonov-Bohm (AB) problem for vector bosons by the Duffin-Kemmer-Petiau (DKP) formalism is analyzed. Depending on the values of the spin projection, the relevant eigenvalue equation coming from the DKP formalism reveals an equivalence to the spin-$1/2$ AB problem. By using the self-adjoint extension approach, we examine the bound state scenario. The energy spectra are explicitly computed as well as their dependencies on the magnetic flux parameter and also the conditions for the occurrence of bound states.