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A symplectic geometric origin of universal quartic modified dispersion relations

Sanjib Dey, Mir Faizal

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.

A symplectic geometric origin of universal quartic modified dispersion relations

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.
Paper Structure (9 sections, 53 equations)

This paper contains 9 sections, 53 equations.

Table of Contents

  1. Introduction
  2. Fedosov-Berezin Quantization
  3. Spectral Geometric
  4. Topos Theory
  5. Phenomenological implications
  6. Conclusion
  7. Appendix A: Fedosov Quantization on Kähler Manifolds
  8. Appendix B: LQG and String Theory as Dual Descriptions
  9. Appendix C: Geometric Origin of the Universal MDR