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  • Open Access

Time-ordering in the Dyson-Unruh problem: Accelerated observers and quantum fields

Arash Azizi*

  • The Institute for Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA

  • *Contact author: sazizi@tamu.edu
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Phys. Rev. D 112, 025006 – Published 7 July, 2025

DOI: https://doi.org/10.1103/cty8-mtt8

Abstract

We develop a systematic framework for analyzing time-ordered perturbative expansions in quantum field theory (QFT) applicable to stationary spacetimes with a timelike Killing vector field. Focusing on the interaction between a scalar field and multiple Unruh-DeWitt detectors undergoing uniform acceleration, we employ the global Killing time to synchronize interactions and consistently implement the Dyson expansion. Our formalism prevents causality-violating errors that arise from a naive treatment of time-ordering for detectors with differing proper times and accelerations. Using light-cone coordinates and explicit parametrizations of the detector worldlines, we construct and classify all relevant interaction terms up to the third order for a two-detector system. This provides a clear and unambiguous foundation for calculating higher-order S-matrix contributions and investigating phenomena such as entanglement harvesting.

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Phys. Rev. D 112, 025006– Published 7 July, 2025
  • Received 3 May 2025
  • Accepted 23 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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