Field quantization in rotating frames: coordinate covariance and the circular-detector response

• URL: http://arxiv.org/abs/2609.10390v1
• Date: Wed, 09 Sep 2026 16:11:50 GMT
• Title: Field quantization in rotating frames: coordinate covariance and the circular-detector response
• Abstract summary: Coordinate-transformed rigid and TT modes span the same positive-frequency subspace as inertial modes.<n>Neither rotating time flow selects a global scalar ground state, although for different reasons.<n>A circular Unruh-DeWitt detector in the Minkowski vacuum has a stationary, nonzero response.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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