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

## TL;DR

This paper develops a method to calculate the anomalous velocity of a spinning electron using Pryce's mass-center operators, linking quantum expectation values to classical motion and identifying key contributing factors.

## Contribution

It introduces a novel approach connecting Dirac equation expectation values with classical electron motion to compute anomalous velocity.

## Key findings

- Identifies two main factors contributing to anomalous velocity.
- Provides a classical expression for the electron's position based on quantum operators.
- Shows the dependence of anomalous velocity on operator choice and rotational effects.

## 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.