Natural Cutoffs via Compact Symplectic Manifolds

TL;DR

This paper investigates how quantum gravity-induced natural cutoffs can be modeled as global properties of compact symplectic manifolds, challenging the idea that local deformations alone suffice.

Contribution

It demonstrates that quantum gravity cutoffs are inherently global (topological) features of symplectic manifolds, not just local Hamiltonian deformations.

Findings

Cutoffs require global deformations of Hamiltonian systems.

Quantum gravity effects are topological properties of symplectic manifolds.

Validated results with Moyal, Snyder, and polymer models.

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.