Generalized uncertainty principle theories and their classical interpretation

In this work, we show that it is possible to define a classical system associated with a Generalized Uncertainty Principle (GUP) theory via the implementation of a consistent symplectic structure. This provides a solid framework for the classical Hamiltonian formulation of such theories and the stud...

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Main Authors: Matteo Bruno, Sebastiano Segreto, Giovanni Montani
Format: Article
Language:English
Published: Elsevier 2024-12-01
Series:Nuclear Physics B
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Online Access:http://www.sciencedirect.com/science/article/pii/S0550321324003055
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author Matteo Bruno
Sebastiano Segreto
Giovanni Montani
author_facet Matteo Bruno
Sebastiano Segreto
Giovanni Montani
author_sort Matteo Bruno
collection DOAJ
description In this work, we show that it is possible to define a classical system associated with a Generalized Uncertainty Principle (GUP) theory via the implementation of a consistent symplectic structure. This provides a solid framework for the classical Hamiltonian formulation of such theories and the study of the dynamics of physical systems in the corresponding deformed phase space.By further characterizing the functions that govern non-commutativity in the configuration space using the algebra of angular momentum, we determine a general form for the rotation generator in these theories and crucially, we show that, under these conditions, unlike what has been previously found in the literature at the quantum level, this requirement does not lead to the superselection of GUP models at the classical level.Finally, we postulate that a properly defined GUP theory can be correctly interpreted classically if and only if the corresponding quantum commutators satisfy the Jacobi identities, identifying those quantization prescriptions for which this holds true.
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spelling doaj-art-032723311dbf41ec83d6faaed8ec3e712025-08-20T02:37:32ZengElsevierNuclear Physics B0550-32132024-12-01100911673910.1016/j.nuclphysb.2024.116739Generalized uncertainty principle theories and their classical interpretationMatteo Bruno0Sebastiano Segreto1Giovanni Montani2Physics Department, Sapienza University of Rome, P.za Aldo Moro 5, Rome, 00185, Italy; INFN, Sezione di Roma 1, P.le Aldo Moro 2, Rome, 00185, ItalyPhysics Department, Sapienza University of Rome, P.za Aldo Moro 5, Rome, 00185, Italy; INFN, Sezione di Roma 1, P.le Aldo Moro 2, Rome, 00185, Italy; Corresponding author.ENEA C.R., Via E. Fermi 45, Frascati, 00044, Italy; Physics Department, Sapienza University of Rome, P.za Aldo Moro 5, Rome, 00185, ItalyIn this work, we show that it is possible to define a classical system associated with a Generalized Uncertainty Principle (GUP) theory via the implementation of a consistent symplectic structure. This provides a solid framework for the classical Hamiltonian formulation of such theories and the study of the dynamics of physical systems in the corresponding deformed phase space.By further characterizing the functions that govern non-commutativity in the configuration space using the algebra of angular momentum, we determine a general form for the rotation generator in these theories and crucially, we show that, under these conditions, unlike what has been previously found in the literature at the quantum level, this requirement does not lead to the superselection of GUP models at the classical level.Finally, we postulate that a properly defined GUP theory can be correctly interpreted classically if and only if the corresponding quantum commutators satisfy the Jacobi identities, identifying those quantization prescriptions for which this holds true.http://www.sciencedirect.com/science/article/pii/S0550321324003055Generalized uncertainty principleSymplectic geometryPoisson structureJacobi identity
spellingShingle Matteo Bruno
Sebastiano Segreto
Giovanni Montani
Generalized uncertainty principle theories and their classical interpretation
Nuclear Physics B
Generalized uncertainty principle
Symplectic geometry
Poisson structure
Jacobi identity
title Generalized uncertainty principle theories and their classical interpretation
title_full Generalized uncertainty principle theories and their classical interpretation
title_fullStr Generalized uncertainty principle theories and their classical interpretation
title_full_unstemmed Generalized uncertainty principle theories and their classical interpretation
title_short Generalized uncertainty principle theories and their classical interpretation
title_sort generalized uncertainty principle theories and their classical interpretation
topic Generalized uncertainty principle
Symplectic geometry
Poisson structure
Jacobi identity
url http://www.sciencedirect.com/science/article/pii/S0550321324003055
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