Few-Body Systems, vol.64, no.3, 2023 (SCI-Expanded)
We introduce an exactly soluble model for a fermion-antifermion pair exposed to magnetic flux in the hyperbolic wormhole. This model is based on an analytical solution of the corresponding two-body Dirac equation. We show a non-perturbative wave equation for such a pair in exactly soluble form. This makes it possible to acquire a complete energy spectrum. Results clearly show the effects of the magnetic flux as well as the wormhole background on the dynamics of the considered pair and such a composite system may behave as a single fermion or a single boson by depending on the magnetic flux. This implies that one can control the dynamics of such a pair in an optical background with constant negative Gaussian curvature.