Localization of relativistic particles and uncertainty relations

Abstract

Localization of relativistic particles and their position-momentum uncertainty relations are not yet fully understood. We discuss two schemes of photon localization that are based on the energy density. One scheme produces a positive operator-valued measure for localization. It coincides with the number density operator and reproduces the effective 3x3 polarization density matrix. Another scheme results in a probability distribution that is conditioned on the detection. In both schemes the uncertainty relations for transversal position and momentum approach the Heisenberg bound $\Delta p\Delta z=\hslash /2$

Published version; significantly modified and corrected with a focus on photons and the experimental consequences

References in corpus (12)

• Continuous variable quantum computation with spatial degrees of freedom of photons
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• Uncertainty relation for photons
• Localized qubits in curved spacetimes
• Heisenberg uncertainty relation for photons
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• Massive Unruh particles cannot be directly observed
• On the Relativistic Spatial Localization for massive real scalar Klein-Gordon quantum particles
• Probability density of relativistic spinless particles
• Proposal for an optical interferometric measurement of the gravitational red-shift with satellite systems
• Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties
• Causal Localizations of the Massive Scalar Boson
• Localization in Quantum Field Theory
• Quantum imaging using relativistic detectors
• Localization POVMs and intrinsic temporal uncertainty
• Non-Heisenbergian quantum mechanics
• Localization of scalar quantum fields on Minkowski space-time
• Non-minimal Coupling from Consistency Requirements for a Localization Operator