Localized States for Elementary Systems
Open accessAbstract
It is attempted to formulate the properties of localized states on the basis of natural invariance requirements. Chief of these is that a state, localized at a certain point, becomes, after a translation, orthogonal to all the undisplaced states localized at that point. It is found that the required properties uniquely define the set of localized states for elementary systems of non-zero mass and arbitrary spin. The localized functions belong to a continuous spectrum of an operator which it is natural to call the position operator. This operator has automatically the property of preserving the positive energy character of the wave function to which it is applied (and it should be applied only to such wave functions). It is believed that the development here presented may have applications in the theory of elementary particles and of the collision matrix.
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The photon and other massless particles cannot be spatially localized.
“It is known that the photon and other massless particles cannot be spatially localized [15,16,56,57].”
From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [15]
In the paragraph on zero-mass equations following Eq. (25) (page not provided), Newton and Wigner report no localized states in their sense for spin 1, which includes photons, and higher finite spins. But they also report localized states for zero-mass spin 0 and spin ½ systems, so the claim overgeneralizes to other massless particles. Their conclusion concerns localization under their stated requirements, not every possible meaning of spatial localization. (LLM, conf=0.91)
Experimental — accuracy not yet measuredThe absence of observable Zitterbewegung for scalar particles and the similarity of Eqs. (57)-(60) for massless and massive particles show that the electrostatic contact interaction is not caused by particle localization.
“An absence of observable Zitterbewegung for scalar particles and a similarity of Eqs. (57)-(60) for massless and massive particles show that it not caused by the particle localization (established in Ref. [15]) either.”
From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [15]
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Lorentz-invariant photon number density
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<i>Zitterbewegung</i> of massless particles
Silenko, A. J. (2022) · Physical Review A · doi:10.1103/physreva.105.062211 · Cited by 11 · see citing works
“It is well-known that the photon and other massless particles cannot be spatially localized [11, 12, 34–36].”
Background
- Authors
- Newton, T. D., & Wigner, E. P.
- Affiliations
- Princeton University (US)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1949-07-01
- Volume
- 21
- Issue
- 3
- Pages
- 400-406
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W1964301336
- Cited by
- 1,394
- References
- 0
- Citations by year
- 2026: 19 · 2025: 44 · 2024: 31 · 2023: 47 · 2022: 33 · 2021: 42 · 2020: 31 · 2019: 33 · 2018: 31 · 2017: 36 · 2016: 35 · 2015: 36 · 2014: 41 · 2013: 43 · 2012: 38
- FWCI
- 2.21
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- localized states, translation invariance, position operator, continuous spectrum, arbitrary spin, elementary particles, collision matrix
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