Semi-local observables, edge modes and quantum reference frames in quantum electromagnetism: an algebraic approach
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| Format: | Preprint |
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2025
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| _version_ | 1866918132075986944 |
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| author | Fewster, Christopher J. Janssen, Daan W. Rejzner, Kasia |
| author_facet | Fewster, Christopher J. Janssen, Daan W. Rejzner, Kasia |
| contents | Boundaries and corners of spacetime play a vital role in understanding physical concepts including entanglement entropy, the infrared problem in QFT and quantum gravity. Standard local quantum field theory struggles to accommodate such boundary-sensitive observables. In this paper we develop an algebraic framework for \emph{semi-local quantum electromagnetism} on finite Cauchy lenses: a class of compact spacetimes with boundaries and corner. At the classical level, we establish a decomposition of the reduced covariant phase space into bulk closed-loop and surface sectors and demonstrate how the covariant phase space approach relates to the Peierls bracket construction commonly used in perturbative algebraic quantum field theory. Upon quantisation, we obtain a Weyl $C^{*}$-algebra of semi-local observables transforming non-trivially under large gauge transformations (those with non-trivial boundary contribution). To recover gauge invariance, we invoke the notion of \emph{quantum reference frames} (QRFs) and construct a relativisation map, where we treat auxiliary surface degrees of freedom as QRFs for the large gauge transformations. The relativisation map is constructed directly on the level of $C^{*}$-algebras, making our construction state-independent. The QRF viewpoint on semi-local observables provides new tools for understanding gauge theories on manifolds with boundary, including the problem of gluing theories on Cauchy lenses with common boundaries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_20939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-local observables, edge modes and quantum reference frames in quantum electromagnetism: an algebraic approach Fewster, Christopher J. Janssen, Daan W. Rejzner, Kasia Mathematical Physics Boundaries and corners of spacetime play a vital role in understanding physical concepts including entanglement entropy, the infrared problem in QFT and quantum gravity. Standard local quantum field theory struggles to accommodate such boundary-sensitive observables. In this paper we develop an algebraic framework for \emph{semi-local quantum electromagnetism} on finite Cauchy lenses: a class of compact spacetimes with boundaries and corner. At the classical level, we establish a decomposition of the reduced covariant phase space into bulk closed-loop and surface sectors and demonstrate how the covariant phase space approach relates to the Peierls bracket construction commonly used in perturbative algebraic quantum field theory. Upon quantisation, we obtain a Weyl $C^{*}$-algebra of semi-local observables transforming non-trivially under large gauge transformations (those with non-trivial boundary contribution). To recover gauge invariance, we invoke the notion of \emph{quantum reference frames} (QRFs) and construct a relativisation map, where we treat auxiliary surface degrees of freedom as QRFs for the large gauge transformations. The relativisation map is constructed directly on the level of $C^{*}$-algebras, making our construction state-independent. The QRF viewpoint on semi-local observables provides new tools for understanding gauge theories on manifolds with boundary, including the problem of gluing theories on Cauchy lenses with common boundaries. |
| title | Semi-local observables, edge modes and quantum reference frames in quantum electromagnetism: an algebraic approach |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2508.20939 |