Impact of relativity on particle localizability and ground state entanglement
arXiv:1902.10684 · doi:10.1088/1751-8121/ab3593
Abstract
Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many known issues with such a description, indicating an answer in the negative. In this paper, we examine these obstructions by tracing how they (partially) subside in passing to an approximation of ordinary quantum mechanics in the non-relativistic regime. We undertake a recovery of the characteristic features of non-relativistic quantum mechanics beyond simply the Schrödinger equation. We find that once this is achieved, there are persisting issues in the localizability of particle states. A major focus is on the lingering discrepancy between two different localization schemes in quantum field theory. The non-relativistic approximation of the quantum field theory is achieved by introducing an ultraviolet cutoff set by the Compton scale. The other main undertaking of this paper is to quantify the fate of ground state entanglement and the Unruh effect in the non-relativistic regime. Observing that the Unruh temperature vanishes in the naive limit as the speed of light is taken to infinity motivates the question: is the Unruh effect relativistic? It happens that this is closely related to the former issues, as ground state entanglement causes obstructions to localizability through the Reeh-Schlieder theorem.
arXiv commentv2: Minor changes, published version
References in corpus (34)
- Peres-Horodecki separability criterion for continuous variable systems
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
- Lorentz invariance with an invariant energy scale
- The Unruh effect and its applications
- Nonstandard optics from quantum spacetime
- Dumb Holes and the Effects of High Frequencies on Black Hole Evaporation
- Entanglement entropy of black holes
- Ultraviolet modifications of dispersion relations in effective field theory
- Bound entangled Gaussian states
- Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
- Hawking Spectrum and High Frequency Dispersion
- Entanglement from the vacuum
- Self-adjoint extensions of operators and the teaching of quantum mechanics
- Harvesting correlations from the quantum vacuum
- Computing the spectrum of black hole radiation in the presence of high frequency dispersion: an analytical approach
- On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
- Continuous Histories and the History Group in Generalised Quantum Theory
- Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis
- The Foldy-Wouthuysen transformation
- Problems with the Newton-Schrödinger Equations
- Instantaneous Spreading and Einstein Causality in Quantum Theory
- A Generalized Shannon Sampling Theorem, Fields at the Planck Scale as Bandlimited Signals
- Continuous Time and Consistent Histories
- Causality, particle localization and positivity of the energy
- Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry
- No place for particles in relativistic quantum theories?
- Frustration, interaction strength and ground-state entanglement in complex quantum systems
- Modified Dispersion Relations from the Renormalization Group of Gravity
- Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
- Obtaining the Non-relativistic Quantum Mechanics from Quantum Field Theory: Issues, Folklores and Facts
- Locality and entanglement in bandlimited quantum field theory
- Renormalized Thermal Entropy in Field Theory
- Local quanta, unitary inequivalence, and vacuum entanglement
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