Pryce's mass-center operators and the anomalous velocity of a spinning electron

Abstract

In the present work, we develop a method to calculate the anomalous velocity of a spinning electron. From Dirac equation, the relationships among the expectation values of the Pryce's mass-center operator, the position operator, the spin operator and the canonical momentum operator are investigated. By requiring that the center of mass for the classical spinning electron is related to the expectation value of the Pryce's mass-center operator, one can obtain a classical expression for the position of the electron. With the classical equations of motion, the anomalous velocity of a spinning electron can be easily calculated. It is shown that two factors contribute to the anomalous velocity: one is dependent on the selection of the Pryce's mass-center operators and the other is a type-independent velocity expressed by the rotational velocity and the Lorentz force.