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Quantum gravity, shadow states, and quantum mechanics
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A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle. Maxwell fields will be discussed in the second paper of this series which further develops the program and provides details.
Forward citations
Cited by 9 Pith papers
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Integral Hilbert spaces and the dynamics of loop quantum cosmos
In a loop quantum cosmology model with negative cosmological constant, semiclassical states built by integrating over all superselection sectors behave no differently from single-sector states, with differences below ...
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Coherent states in minimal-length Quantum Mechanics: inequivalent characterizations and emergent squeezing
Minimal length via GUP makes the usual coherent state characterizations inequivalent for the harmonic oscillator, deforming phase-space trajectories and inducing intrinsic squeezing absent in standard quantum mechanics.
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Bounded compactness from G(E)UP
The generalized uncertainty principle bounds the compactness of any object much heavier than the Planck mass by about 1/α, and the existence of black holes forces the GUP parameter to satisfy α ≲ 2.
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Kinematical correlations via $\kappa$-Poincar\'e coproducts
In the classical basis the non-bijective momentum map induces branch-dependent κ-deformed back-to-back correlations for two-particle states obeying vanishing total momentum.
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Generalising gravitationally induced decoherence beyond linear environmental interactions in a microscopic quantum mechanical toy model
Extends linear toy model of gravitational decoherence to sinus-like Weyl couplings, derives master equation via two correlation-function methods, and solves the renormalised equation.
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The problem of time: a path integral view
In a path-integral model of timeless quantum systems, time evolution arises when a clock is prepared in a semiclassical state, showing that the cosine problem in quantum gravity follows from time-reversal invariance a...
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Classical Polymerization of the Bianchi I Model with Deformed Poisson Structure
An exponential Poisson-deformation in polymerized Bianchi I turns the volume collapse logarithmic and can bound the anisotropies — but the paper attaches its boundedness threshold to the wrong end of the evolution.
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Polymer Bianchi-I with polymer matter
In a Bianchi-I universe with polymer quantization of both geometry and a massless scalar, the matter polymer scale shifts the quantum bounce and alters volume and anisotropy evolution.
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Response of a uniformly accelerated Unruh-DeWitt detector in polymer quantization
In polymer quantization, a uniformly accelerated Unruh-DeWitt detector sees a non-thermal vacuum response that can be mimicked by the Fock-space two-point function with a finite regulator ε≈2.16 instead of the usual ε...
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