Natural cutoffs via compact symplectic manifolds

In the context of phenomenological models of quantum gravity, it is claimed that ultraviolet (UV) and infrared (IR) natural cutoffs can be realized from local deformations of the Hamiltonian systems. In this paper, we scrutinize this hypothesis and formulate a cutoff-regularized Hamiltonian system....

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Bibliographic Details
Published in:Classical and quantum gravity 2016-01, Vol.33 (2), p.25009-25029
Main Authors: Nozari, K, Gorji, M A, Hosseinzadeh, V, Vakili, B
Format: Article
Language:English
Subjects:
Deformation
Hamiltonian functions
Infrared
Manifolds
Manifolds (mathematics)
natural cutoffs
Quantum gravity
symplectic manifold
Topology
Ultraviolet
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Summary:In the context of phenomenological models of quantum gravity, it is claimed that ultraviolet (UV) and infrared (IR) natural cutoffs can be realized from local deformations of the Hamiltonian systems. In this paper, we scrutinize this hypothesis and formulate a cutoff-regularized Hamiltonian system. The results show that while local deformations are necessary to have cutoffs, they are not sufficient. In fact, the cutoffs can be realized from globally-deformed Hamiltonian systems that are defined on compact symplectic manifolds. By taking the universality of quantum gravity effects into account, we then conclude that quantum gravity cutoffs are global (topological) properties of the symplectic manifolds. We justify our results by considering three well-known examples: the Moyal, Snyder and polymer-deformed Hamiltonian systems.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/33/2/025009