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arXiv · 2603.16532

A symplectic geometric origin of universal quartic modified dispersion relations

Sanjib Dey·Mir Faizal
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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.

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Sanjib Dey, Mir Faizal. 2026-03-17. A symplectic geometric origin of universal quartic modified dispersion relations. https://doi.org/10.1016/j.physletb.2026.140356

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