Classical perspectives on the NewtonWigner position observable
Abstract
This paper deals with the NewtonWigner position observable for Poincaréinvariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the wellknown NewtonWigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the NewtonWigner position as “center of spin”, already proposed by Fleming in 1965 again in the quantum context.
 Publication:

International Journal of Geometric Methods in Modern Physics
 Pub Date:
 2020
 DOI:
 10.1142/S0219887820501765
 arXiv:
 arXiv:2004.09723
 Bibcode:
 2020IJGMM..1750176S
 Keywords:

 Position observable;
 localization;
 Poincaré invariance;
 elementary systems;
 Newton–Wigner position;
 Hamiltonian mechanics;
 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 Physics  History and Philosophy of Physics;
 37J39;
 70H33;
 83A05
 EPrint:
 28+5+4 pages (main text, references, appendices), to appear in International Journal of Geometric Methods in Modern Physics. v2: Added references, corrected typos, restructured references v3: Corrected typos, changed MSC class (betterfitting class in MSC2020)