On the Uniqueness of the Newton-Wigner Position Operator

TL;DR

This paper proves that the Newton-Wigner position operator is uniquely determined under a specific quantum covariance condition, clarifying its foundational role in relativistic quantum mechanics.

Contribution

It establishes the uniqueness of the Newton-Wigner position operator by imposing a quantum manifest covariance condition within the Hamiltonian formalism.

Findings

Uniqueness of the Newton-Wigner operator is demonstrated.

The covariance condition constrains the operator's form.

Clarifies foundational aspects of relativistic quantum position operators.

Abstract

It is shown that the quantum position operator of Newton and Wigner for non-zero mass systems is uniquely determined if one imposes a quantum ''manifest covariance'' condition of the same type as the similar condition of Currie, Jordan and Sudarshan in the the framework of the Hamiltonian formalism.