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.
Quantum gravity, shadow states, and quantum mechanics
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
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.
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2026 6verdicts
UNVERDICTED 6representative citing papers
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.
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.
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 and neutral boundary conditions.
GUP with minimal length and maximal momentum applied to Schwarzschild black holes yields finite discrete mass spectrum, maximum mass, and constrains the GUP parameter to β ≲ 10^{-98} from astrophysical data.
GUP deformation shortens Kasner epochs in the Mixmaster universe while polymerization lengthens them, with combined effects adding linearly and chaos strength depending on the deformation parameters.
citing papers explorer
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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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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 and neutral boundary conditions.
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Finite Hilbert space and maximum mass of Schwarzschild black holes from a Generalized Uncertainty Principle
GUP with minimal length and maximal momentum applied to Schwarzschild black holes yields finite discrete mass spectrum, maximum mass, and constrains the GUP parameter to β ≲ 10^{-98} from astrophysical data.
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Chaos and epoch structure in the deformed Mixmaster universe
GUP deformation shortens Kasner epochs in the Mixmaster universe while polymerization lengthens them, with combined effects adding linearly and chaos strength depending on the deformation parameters.