Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Classical perspectives on the Newton--Wigner position observable

Giulini, Domenico

Published Apr 22, 2020• 8 citations
OpenAlex

Abstract

This paper deals with the Newton--Wigner position observable for Poincaré invariant \emph{classical}systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton--Wigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the Newton--Wigner position as `centre of spin', already proposed by Fleming in 1965 again in the quantum context.

Related papers

Classical perspectives on the Newton–Wigner position observable

Philip K. Schwartz, Domenico Giulini

This paper deals with the Newton–Wigner position observable for Poincaré-invariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton–Wigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the Newton–Wigner position as “center of spin”, already proposed by Fleming in 1965 again in the quantum context.

arXiv:2004.09723•International Journal of Geometric Methods in Modern Physics•Aug 12, 2020•6 citations

General expressions for the position and spin operators of relativistic systems

Miguel Lorente, P. Román

Some general assumptions based on the physical properties of elementary and of composite quantized systems lead in a natural way to general expressions for the position and spin operators of massive particles. All previously proposed position and spin operators, defined in the enveloping algebra of the Poincaré group, appear as special cases. By algebraic arguments a general local position operator is obtained which is proved to coincide under special conditions with the Pryce-Newton-Wigner position operator.

Journal of Mathematical Physics•Jan 1, 1974•31 citations

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

Taeseung Choi

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.

arXiv:1412.0351•Dec 1, 2014•0 citations

Localization in Relativistic Quantum Theories

Lars O. Herrmann

Although the concept of localization in non-relativistic quantum mechanics is mathematically well-defined there is no obvious and unambiguous way to generalize it to relativistic quantum theory. After a brief review of localization in quantum mechanics the Newton-Wigner localization scheme is introduced and it is shown by the example of a massive spinless system how it leads to a position operator with seemingly unphysical properties. This motivated the development of several theorems which claim to rule out the existence of localizable particles. A particularly important one of them is presented and its validity discussed. In the last section however it is shown that if localization is considered with respect to spacelike hyperplanes, the properties of the Newton-Wigner position operators are not necessarily unphysical and localizable particles can exist.

•Jun 1, 2010•5 citations

On the Uniqueness of the Newton-Wigner Position Operator

D. R. Grigore

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.

arXiv:hep-th/9302087•Feb 19, 1993•0 citations

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

Taeseung Choi

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

Journal of the Korean Physical Society•Mar 1, 2015•4 citations
This paper deals with the Newton--Wigner position observable for Poincaré invariant \emph{classical}systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton--Wigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the Newton--Wigner position as `centre of spin', already proposed by Fleming in 1965 again in the quantum context.
Some general assumptions based on the physical properties of elementary and of composite quantized systems lead in a natural way to general expressions for the position and spin operators of massive particles. All previously proposed position and spin operators, defined in the enveloping algebra of the Poincaré group, appear as special cases. By algebraic arguments a general local position operator is obtained which is proved to coincide under special conditions with the Pryce-Newton-Wigner position operator.
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.
Although the concept of localization in non-relativistic quantum mechanics is mathematically well-defined there is no obvious and unambiguous way to generalize it to relativistic quantum theory. After a brief review of localization in quantum mechanics the Newton-Wigner localization scheme is introduced and it is shown by the example of a massive spinless system how it leads to a position operator with seemingly unphysical properties. This motivated the development of several theorems which claim to rule out the existence of localizable particles. A particularly important one of them is presented and its validity discussed. In the last section however it is shown that if localization is considered with respect to spacelike hyperplanes, the properties of the Newton-Wigner position operators are not necessarily unphysical and localizable particles can exist.
A relativistic spin operator is the difference between the total and the orbital angular momentum. As the unique position operator for a localized state, the remarkable Newton-Wigner position operator, which has all the desirable commutation relations of a position operator, can give a proper spin operator. Historically, the three important spin operators proposed by Bogolubov et al. , Pryce, and Foldy-Woutheysen, respectively were investigated to manifest a spin operator corresponding to the Newton-Wigner position operator. We clarify a unique spin operator in relativistic quantum mechanics, which can be described by using the Dirac Hamiltonian.