Newton-Wigner position operator and its corresponding spin operator in relativistic quantum mechanics

TL;DR

This paper investigates the Newton-Wigner position operator and its associated spin operator in relativistic quantum mechanics, clarifying their properties and relationships within the Dirac framework.

Contribution

It identifies a unique relativistic spin operator linked to the Newton-Wigner position operator, clarifying their roles in Dirac theory.

Findings

The Newton-Wigner position operator has desirable commutation relations.

A unique relativistic spin operator is established.

Historical spin operators are analyzed in relation to the Newton-Wigner operator.

Abstract

A relativistic spin operator is to be the difference between the total and orbital angular momentum. As the unique position operator for a localized state, the remarkable Newton-Wigner position operator, which has all desirable commutation relations as a position operator, can give a proper spin operator. Historically important three spin operators respectively proposed by Bogolubov et al., Pryce, and Foldy-Woutheysen are investigated to manifest a corresponding spin operator to the Newton-Wigner position operator. We clarify a unique spin operator in relativistic quantum mechanics described by the Dirac Hamiltonian.