Generalized quaternionic free rotational Dirac equation and spinor solutions in the electromagnetic field

Abstract

Starting with the quaternionic Minkowski space–time and its four-vector representation, a rotational analogue of the quaternionic Dirac equation in the electromagnetic field is developed, which includes not only the energy solutions but also the angular momentum solutions for rotating Dirac fermions. The striking feature of the quaternionic approach is that it depicts a unified representation of energy–momentum in a single framework as the space–time. Furthermore, we establish the generalized Schrodinger–Pauli-like equation associated with generalized electric and magnetic dipole energies that corresponds to their dipole moments. As such, the present analysis deals with the invariant behavior of the extended quaternionic rotational Dirac equation under Lorentz–Poincaré, Gauge, duality, and CPT invariance.