Dirac Wave Functions of Positive Energy with Arbitrarily Small Position Uncertainty

arXiv:2603.04569 · quant-ph · Submitted 2026-03-04 · Read on arXiv

quant-ph

Submitted: 2026-03-04

Updated: 2026-07-03

Comments: 20 pages LaTeX, 3 figure files; v3: Section 5 (on related works) added, minor improvements throughout the paper

Journal ref: Proceedings of the Royal Society A 482(2346): 20260203 (2026)

DOI: 10.1098/rspa.2026.0203

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Hilbert Space — 3× in this paper · explained in 2 episodes
• Superradiance — 1× in this paper · explained in 3 episodes

Sources

• Lorentz-covariance of Position Operator and its Eigenstates for a massive spin $1/2$ field
• Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties
• Spatial Localization of Relativistic Quantum Systems: The Commutativity Requirement and the Locality Principle. Part I: A General Analysis
• Spatial Localization of Relativistic Quantum Systems: The Commutativity Requirement and the Locality Principle. Part II: A Model from Local QFT
• Twisted Localized Solutions of the Dirac Equation: Hopfion-like States of Relativistic Electrons
• Comment on "Possibility of small electron states"

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