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 ηη-pseudo-Hermitian with respect to certain metric operators ηη. 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.

► New pseudo-Hermitian generalizations of the Dirac oscillator (DO) are presented.
► Exact solutions for two examples of pseudo-Hermitian interactions are found.
► The real spectrum and the wavefunctions are given.
► A pseudo-Hermitian generalization of the Jaynes–Cummings (JC) quantum optical model is given.
► Using spin flipping, the relation to the anti-JC optical model is discussed.