Wave-packet view of the Dirac electron

TL;DR

This paper models the Dirac electron as a wavepacket to clarify its behavior in weak electromagnetic fields, revealing intrinsic spin magnetic moments from self-rotation and deriving an effective Hamiltonian with relativistic corrections.

Contribution

It introduces a wavepacket perspective of the Dirac electron, linking intrinsic spin to wavepacket self-rotation and deriving an effective Hamiltonian with all-order relativistic corrections.

Findings

Intrinsic spin magnetic moment from wavepacket self-rotation

Non-canonical equations due to non-Abelian geometric phases

Effective Hamiltonian reproduces Pauli Hamiltonian with relativistic corrections

Abstract

By viewing the electron as a wavepacket in the positive energy spectrum of the Dirac equation, we are able to achieve a much clearer understanding of its behavior under weak electromagnetic fields. The intrinsic spin magnetic moment is found to be established from the self-rotation of the wavepacket. A non-canonical structure is also exhibited in the equations of motion due to non- Abelian geometric phases of the Dirac spinors. The wavepacket energy can be expressed simply in terms of the kinetic, electrostatic, and Zeeman terms only. This can be transformed into an effective quantum Hamiltonian by a novel scheme, and reproduces the Pauli Hamiltonian with all-order relativistic corrections.