Semiclassical state on algebra of observables for de Sitter space and time reversal symmetry
Abstract
In de Sitter static patch holography, coupling bulk quantum fields to an observer's dynamical clock yields a type II1 von Neumann algebra ℳ+ of gauge-invariant observables. However, the unique tracial state on this algebra fails to reproduce semiclassical bulk correlation functions. We resolve this issue by introducing a family of heavy-clock states, representing an observer reference frame with heavy inertia. We prove that in the heavy-clock limit, n-point correlation functions of gauge-invariant dressed observables reproduce the bulk quantum field correlation functions on de Sitter spacetime. Furthermore, we investigate a generalized observer Hamiltonian Ĥobs=|π̂| that incorporates both forward-running (π≥ 0) and backward-running (π<0) clocks. The resulting von Neumann algebra ℳ of gauge-invariant observables remains a type~II1 factor and is isomorphic to ℳ+⊗ M2(ℂ), where M2(ℂ) is the algebra of 2×2 complex matrices transforming between the two clock orientations. Time-reversal symmetry is implemented in this setting as an anti-unitary operator that exchanges the two clock orientations, yielding a type~II1 von Neumann algebra ℱ of gauge-invariant, time-reversal-invariant observables. We generalize the heavy-clock state construction to both ℳ and ℱ, showing that n-point correlation functions calculated in heavy-clock states match the corresponding semiclassical bulk correlation functions. Finally, by coupling Einstein gravity to the Brown--Kuchař dust field, we derive the observer Hamiltonian Ĥobs=|π̂| from a perturbative reduction along the observer's worldline in the G → 0 limit. This provides a field-theoretic foundation for the observer model developed in this work.
Related
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BibTeX
@misc{han2026semiclassical,
title = {{Semiclassical state on algebra of observables for de Sitter space and time reversal symmetry}},
author = {Muxin Han and Yichen Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14175},
eprint = {2610.14175},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14175},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Semiclassical state on algebra of observables for de Sitter space and time reversal symmetry
AU - Muxin Han
AU - Yichen Hu
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14175
UR - https://arxiv.org/abs/2610.14175
AB - In de Sitter static patch holography, coupling bulk quantum fields to an observer's dynamical clock yields a type II_1 von Neumann algebra ℳ_+ of gauge-invariant observables. However, the unique tracial state on this algebra fails to reproduce semiclassical bulk correlation functions. We resolve this issue by introducing a family of heavy-clock states, representing an observer reference frame with heavy inertia. We prove that in the heavy-clock limit, n-point correlation functions of gauge-invariant dressed observables reproduce the bulk quantum field correlation functions on de Sitter spacetime. Furthermore, we investigate a generalized observer Hamiltonian Ĥ_obs=|π̂| that incorporates both forward-running (π≥ 0) and backward-running (π<0) clocks. The resulting von Neumann algebra ℳ of gauge-invariant observables remains a type~II_1 factor and is isomorphic to ℳ_+⊗ M_2(ℂ), where M_2(ℂ) is the algebra of 2×2 complex matrices transforming between the two clock orientations. Time-reversal symmetry is implemented in this setting as an anti-unitary operator that exchanges the two clock orientations, yielding a type~II_1 von Neumann algebra ℱ of gauge-invariant, time-reversal-invariant observables. We generalize the heavy-clock state construction to both ℳ and ℱ, showing that n-point correlation functions calculated in heavy-clock states match the corresponding semiclassical bulk correlation functions. Finally, by coupling Einstein gravity to the Brown--Kuchař dust field, we derive the observer Hamiltonian Ĥ_obs=|π̂| from a perturbative reduction along the observer's worldline in the G → 0 limit. This provides a field-theoretic foundation for the observer model developed in this work.
ER -