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

TL;DR

This paper develops a quaternionic rotational Dirac equation in electromagnetic fields, unifying energy-momentum and angular momentum solutions for rotating fermions, and explores its invariance properties.

Contribution

It introduces a generalized quaternionic rotational Dirac equation incorporating electromagnetic interactions and unified energy-momentum representation.

Findings

Derivation of energy and angular momentum solutions for rotating Dirac fermions.

Establishment of a generalized Schrödinger-Pauli-like equation with dipole energies.

Demonstration of invariance under Lorentz, gauge, duality, and CPT transformations.

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 corresponding to their dipole moments. As such, the present analysis deals with the invariant behavior of the extended quaternionic rotational Dirac equation under Lorentz, gauge, duality, and CPT invariance.