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.
Polymer quan tum mechanics and its continuum limit
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abstract
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle and a simple cosmological model.
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2026 5representative citing papers
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.
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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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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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.
- Polymer quantum mechanics on compact configuration spaces