Pseudo-Hermitian generalized Dirac oscillators

We study generalized Dirac oscillators with complex interactions in (1+1)$(1+1)$ dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are η$\eta$-pseudo-Hermitian with respect to certain metric operators η$\eta$. Exact solutions for the generalized Dirac oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with an anti-Jaynes–Cummings-type model and by spin flipping they can also be identified with a Jaynes–Cummings-type model.