An Angular Velocity Operator for the Dirac Equation

The quantum mechanical description of rotation angle and angular velocity has received some attention in the non-relativistic domain. A non-relativistic rotation angle operator was proposed by Barnett and Pegg [Phys. Rev. A 41, 3427 (1990)]. The commutativity of rotation angle operators was investigated by Loss and Mullin [J. Phys. A: Math. Gen. 25 L235 (1992)], and an angular velocity operator was constructed by Abe [Phys Rev A 54/1, 93 (1996)]. All such treatments of angle and angular velocity operators have been non-relativistic. In this paper we derive a relativistic angular velocity operator for the Dirac Hamiltonian. This angular velocity operator is related to the position operator for the Dirac electron suggested by Barut and Malin [Rev. Mod. Phys. 40 (1968) 632], and Barut and Bracken [Phys. Rev. D 23 (1981) 2454]. The angular velocity operator so obtained is shown to yield the anomalous magnetic moment of the electron through an application of second order perturbation theory, where the free electron Dirac Hamiltonian is perturbed by a weak magnetic field.