Fermion-antifermion pair in magnetized optical wormhole background

Abstract

We are interested in a fermion-antifermion pair in magnetized 2+1 dimensional optical background with constant negative curvature. One implements this background for obtaining the optical metric of the BTZ black hole similar to the hyperbolic wormhole. To analyze the evolution of the considered system, we start with constructing the corresponding form of a one-time fully-covariant many-body Dirac equation derived from quantum electrodynamics. The associated equation leads 4×4 dimensional matrix equation resulting in a set of coupled equations consisting of four first-order equations since the two-body equation possesses spin algebra constructed through the Kronecker product of the generalized Dirac matrices. Also, we show a nonperturbative wave equation for the considered system. Accordingly, we seek analytical solutions to the wave equation. We obtain that relativistic energy of the system depends on the parameters of the background as well as the magnetic field. Also, we adapt the results to a Weyl pair. Our results imply that the lifetime of such a pair can be actively tuned, in principle.