A symplectic geometric origin of universal quartic modified dispersion relations

TL;DR

This paper demonstrates that universal quartic modifications to relativistic dispersion relations can be derived from deformation-quantized phase spaces with specific symplectic and complex structures, revealing a geometric origin tied to quantum gravity effects.

Contribution

It introduces a geometric framework showing that quartic dispersion relation modifications naturally emerge from deformation-quantized phase spaces with symplectic and complex structures, unifying multiple approaches.

Findings

Quartic dispersion modifications are linked to symplectic geometric structures.

Three independent methods confirm the universality of the quartic correction.

The correction is governed by a single geometric length scale.

Abstract

We show that quartic modifications of relativistic dispersion relations arise generically from deformation-quantized phase spaces under minimal kinematical assumptions relevant to quantum gravity. When the kinematics admits an integral symplectic structure, a compatible almost-complex structure, and a gauge-invariant two-form sector, the leading Planck-scale correction is controlled by a single geometric length scale. We establish this result through three independent approaches: Fedosov-Berezin quantization, spectral geometry, and a topos-theoretic formulation, all of which yield the same quartic correction and clarify the origin of its apparent universality.