Classical perspectives on the Newton-Wigner position observable
Abstract
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.
- Publication:
-
International Journal of Geometric Methods in Modern Physics
- Pub Date:
- 2020
- DOI:
- 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
- E-Print:
- 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 (better-fitting class in MSC2020)