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A Hilbert Module Approach to Classical and Quantum Reference Frames

  • Lucus Brady
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Abstract

In this paper, we present a model for classical and quantum reference frames for C*-algebras by utilizing Hilbert modules and equivariant correspondences of C*-dynamical systems. We show the classical model provides a commutative baseline for the quantum model, and we discuss how the quantum model encodes the Hilbert space operational formulation of quantum reference frames. We also include various explicit examples for both classical and quantum reference frames.

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Cite

BibTeXRIS
BibTeX
@misc{brady2026hilbert,
  title = {{A Hilbert Module Approach to Classical and Quantum Reference Frames}},
  author = {Lucus Brady},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01894},
  eprint = {2609.01894},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01894},
}
RIS
TY  - UNPB
TI  - A Hilbert Module Approach to Classical and Quantum Reference Frames
AU  - Lucus Brady
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.01894
UR  - https://arxiv.org/abs/2609.01894
AB  - In this paper, we present a model for classical and quantum reference frames for C^*-algebras by utilizing Hilbert modules and equivariant correspondences of C^*-dynamical systems. We show the classical model provides a commutative baseline for the quantum model, and we discuss how the quantum model encodes the Hilbert space operational formulation of quantum reference frames. We also include various explicit examples for both classical and quantum reference frames.
ER  -