Quantum geometry of gravitons

arXiv:2609.15237v1 Announce Type: cross Abstract: We uncover the quantum geometric structure of graviton Wigner functions and stress-energy tensors via quantum field theory in curved spacetime, revealing the phase-space geometry of spacetime and relativistic quantum-state manifolds. We show that the polarization mode expansion of the underlying graviton field operator is fully captured by quantum geometry, as encoded in the spinor-helicity formalism, thereby establishing the geometric framework from the outset. Applying this to a weak gravitational background, we demonstrate the roles of the quantum metric and connection in describing graviton transport beyond the chiral vortical effect. We also clarify the role of the quantum metric in normalizing the perfect-fluid graviton stress tensor within this approach. This work paves the path for explorations of multistate Hilbert-space geometry in high-energy and gravitational physics. In addition, this framework naturally encompasses lower-spin excitations, allowing for a unified quantum geometric treatment of bosonic and fermionic many-body systems in condensed matter and particle physics.

Abstract:We uncover the quantum geometric structure of graviton Wigner functions and stress-energy tensors via quantum field theory in curved spacetime, revealing the phase-space geometry of spacetime and relativistic quantum-state manifolds. We show that the polarization mode expansion of the underlying graviton field operator is fully captured by quantum geometry, as encoded in the spinor-helicity formalism, thereby establishing the geometric framework from the outset. Applying this to a weak gravitational background, we demonstrate the roles of the quantum metric and connection in describing graviton transport beyond the chiral vortical effect. We also clarify the role of the quantum metric in normalizing the perfect-fluid graviton stress tensor within this approach. This work paves the path for explorations of multistate Hilbert-space geometry in high-energy and gravitational physics. In addition, this framework naturally encompasses lower-spin excitations, allowing for a unified quantum geometric treatment of bosonic and fermionic many-body systems in condensed matter and particle physics.

7+15 pages. Comments appreciated

High Energy Physics - Theory (hep-th); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)

arXiv:2609.15237 [hep-th]

(or arXiv:2609.15237v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2609.15237 arXiv-issued DOI via DataCite (pending registration)

From: M. Mehraeen [view email] [v1] Mon, 14 Sep 2026 08:56:08 UTC (96 KB)

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Quantum geometry of gravitons

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