Natural Cutoffs via Compact Symplectic Manifolds

Abstract

In the context of phenomenological models of quantum gravity, it is claimed that the ultraviolet and infrared 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.

17 pages, Revised Version

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• More on the initial singularity problem in gravity's rainbow cosmology
• Compact phase space, cosmological constant, discrete time
• Reconciling a quantum gravity minimal length with lack of photon dispersion
• Bounds on quantum gravity parameter from the $SU(2)$ NJL effective model of QCD
• Classical polymerization of the Schwarzschild metric
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Late time cosmic acceleration from natural infrared cutoff?
• On Gravitational Entropy of de Sitter Universe
• The role of an invariant IR cutoff in late time cosmological dynamics
• Emergent entropy of exotic oscillators and squeezing in three-wave mixing process
• Minisuperspace model of compact phase space gravity
• Entropy bound for the photon gas in noncommutative spacetime
• Early universe thermostatistics in curved momentum spaces
• Black hole thermodynamics in Snyder phase space
• Photon gas thermodynamics in dS and AdS momentum spaces
• Remark on Remnant and Residue Entropy with GUP
• Thermodynamic analysis of a compact object in Rastall-Rainbow gravity
• A note on Hilbert Space Representation of Quantum Mechanics with Minimal Length
• Classical Polymerization of the Bianchi I Model with Deformed Poisson Structure