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Squeezed gravitons and one-loop self-energy under light-cone smearing

Hiroki Matsui1,2,3,4,*

  • 1Osaka Central Advanced Mathematical Institute (OCAMI), Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi, Osaka 558-8585, Japan
  • 2Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui, Tokyo 156-8550, Japan
  • 3Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
  • 4TRIP Headquarters, RIKEN, Wako 351-0198, Japan

  • *Contact author: hiroki.matsui@yukawa.kyoto-u.ac.jp
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Phys. Rev. D 114, 045028 – Published 27 August, 2026

DOI: https://doi.org/10.1103/z1z6-8c8b

Abstract

We investigate light-cone smearing induced by quantum fluctuations of gravitons and its implications for the ultraviolet structure of quantum field theory. By treating the first-order correction to Synge’s world function as an operator, we show that the retarded Green’s function is smeared by the variance of graviton fluctuations. The smearing width depends on the quantum state of gravitons: vacuum fluctuations generate a Gaussian smearing of the light cone, coherent states shift the light-cone position, and squeezed states modify the smearing width itself. We then apply the smeared Feynman propagator to one-loop self-energies in interacting scalar field theories. Within a phenomenological finite-resolution prescription that keeps the effective width nonzero, the ultraviolet-sensitive short-distance terms in the ϕ3 bubble and ϕ4 tadpole diagram expressions are finite. For the illustrative choice that the coarse-graining scale is the Planck length, primordial gravitons induce a relative correction of order 10−10 to the one-loop self-energy. Our results suggest that the quantum state of gravitons can leave a finite imprint on the causal and short-distance structure of quantum field theory.

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Phys. Rev. D 114, 045028– Published 27 August, 2026
  • Received 29 May 2026
  • Accepted 5 August 2026
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