Field quantization in rotating frames: coordinate covariance and the circular-detector response
Abstract
We provide a unified analysis of scalar-field quantization and detector response in relativistic rotating frames, comparing rigid and Trocheris-Takeno (TT) descriptions in unbounded Minkowski spacetime. We distinguish three questions that are often conflated: (i) how a fixed quantum state is represented in rotating coordinates, (ii) whether rotating time evolution selects a global ground state, and (iii) how a rotating detector responds to the vacuum. Coordinate-transformed rigid and TT modes span the same positive-frequency subspace as inertial modes: their Bogoliubov beta coefficients vanish and their mode sums reproduce the Minkowski Wightman function. Neither rotating time flow selects a global scalar ground state, although for different reasons: the rigid generator is not globally timelike and is unbounded below, whereas TT time translation is not a Killing symmetry. Nevertheless, a circular Unruh-DeWitt detector in the Minkowski vacuum has a stationary, nonzero response. We relate this response to negative corotating frequencies, evaluate it after an explicit Hadamard subtraction, and show that it is nonthermal. Thus vanishing Bogoliubov mixing, the absence of a symmetry-selected rotating vacuum, and detector excitation are mutually consistent.
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BibTeX
@misc{junior2026field,
title = {{Field quantization in rotating frames: coordinate covariance and the circular-detector response}},
author = {Sidney Natzuka Junior and Carlos Augusto Domingues Zarro and Matheus dos Santos Soares},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10390},
eprint = {2609.10390},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10390},
}
RIS
TY - UNPB
TI - Field quantization in rotating frames: coordinate covariance and the circular-detector response
AU - Sidney Natzuka Junior
AU - Carlos Augusto Domingues Zarro
AU - Matheus dos Santos Soares
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10390
UR - https://arxiv.org/abs/2609.10390
AB - We provide a unified analysis of scalar-field quantization and detector response in relativistic rotating frames, comparing rigid and Trocheris-Takeno (TT) descriptions in unbounded Minkowski spacetime. We distinguish three questions that are often conflated: (i) how a fixed quantum state is represented in rotating coordinates, (ii) whether rotating time evolution selects a global ground state, and (iii) how a rotating detector responds to the vacuum. Coordinate-transformed rigid and TT modes span the same positive-frequency subspace as inertial modes: their Bogoliubov beta coefficients vanish and their mode sums reproduce the Minkowski Wightman function. Neither rotating time flow selects a global scalar ground state, although for different reasons: the rigid generator is not globally timelike and is unbounded below, whereas TT time translation is not a Killing symmetry. Nevertheless, a circular Unruh-DeWitt detector in the Minkowski vacuum has a stationary, nonzero response. We relate this response to negative corotating frequencies, evaluate it after an explicit Hadamard subtraction, and show that it is nonthermal. Thus vanishing Bogoliubov mixing, the absence of a symmetry-selected rotating vacuum, and detector excitation are mutually consistent.
ER -