标题： 半局部可观测量、边缘模式和量子参考系在量子电动力学中的代数方法 显示英文标题

标题： Semi-local observables, edge modes and quantum reference frames in quantum electromagnetism: an algebraic approach

摘要： 时空的边界和角在理解包括纠缠熵、QFT和量子引力中的红外问题等物理概念中起着至关重要的作用。标准的局部量子场论难以容纳这些对边界敏感的可观测量。在本文中，我们开发了一个代数框架，用于有限柯西透镜上的\emph{半局部量子电动力学}：一类具有边界和角的紧致时空。在经典层面上，我们建立了约化协变相空间的分解，分为体闭合环和表面部分，并展示了协变相空间方法如何与微扰代数量子场论中常用的佩尔斯括号构造相关联。在量化之后，我们得到了一个半局部可观测量的韦尔$C^{*}$-代数，在大规范变换（那些具有非平凡边界贡献的变换）下非平凡地变换。为了恢复规范不变性，我们引入了\emph{量子参考系}（QRFs）的概念，并构建了一个相对化映射，在该映射中，我们将辅助表面自由度视为大规范变换的QRFs。相对化映射直接在$C^{*}$-代数层面上构建，使我们的构造与状态无关。对半局部可观测量的QRF观点为理解带有边界的流形上的规范理论提供了新工具，包括将具有共同边界的柯西透镜上的理论进行粘合的问题。 显示英文摘要

摘要： 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.