Fermion-Antifermion Pair Exposed to Magnetic Flux in an Optical Wormhole

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.

Automated summary

We present a soluble model to study the behavior of a fermion-antifermion pair in the presence of a magnetic flux and a hyperbolic wormhole. By obtaining an analytic solution for the two-body Dirac equation, we derive a non-perturbative wave equation that provides a complete energy spectrum. Our results demonstrate the influence of the magnetic flux and the wormhole background on the dynamics of the pair, revealing that the composite system can exhibit either fermionic or bosonic behavior depending on the magnitude of the magnetic flux. This suggests the potential for controlling the dynamics of such a pair in an optical background with constant negative Gaussian curvature.