发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究将区间量子力学方法扩展到代数量子场论，提出区间代数量子场论，通过开发包约简等方法，重新表述AQFT主要结构特征，证明有限精度下相关特性仍存在，还恢复了因子分类等，提供了相对论量子理论的有限精度统一表述。
AI 中文摘要
近期工作引入了区间量子力学（IQM），这是一个有限精度框架，其中物理信息由可能状态集而非精确状态表示。我们通过引入区间代数量子场论（IAQFT）将此方法扩展到代数量子场论（AQFT），其基本对象是量子包：状态空间的弱*开凸区域，编码从有限多个局部观测获得的有限精度信息。我们开发了包约简和测量更新，建立了有限维信息收缩结果，并通过兼容包网络来表述局域性。AQFT的主要结构特征被用包理论术语重新表述，包括瑞赫 - 施利德性质、哈格定理、模理论、KMS条件和昂鲁效应。我们表明在有限精度下类空真空关联和严格的贝尔不等式违反仍然存在，并且晶格近似与包框架兼容。最后，我们从极限包的几何结构中恢复了因子的默里 - 冯·诺依曼分类以及II₁型因子中的迹和投影等价性。IAQFT因此为相对论量子理论的操作、模和算子代数结构提供了统一的有限精度表述。
英文摘要
We develop Interval Algebraic Quantum Field Theory (IAQFT), a finite-precision operational formulation of algebraic quantum field theory (AQFT). Physical experiments provide only finitely many observations at finite resolution and therefore determine regions of compatible states rather than uniquely specified point states. IAQFT represents this information by quantum parcels---non-empty convex weak$^*$ open regions of state space---with observational parcels determined by finitely many finite-precision expectation constraints. Exact AQFT states remain indispensable mathematical objects and are recovered under appropriate parcel refinement. We establish reduction to exact states, measurement update and no-signalling, and formulate locality through compatible parcel nets. In finite dimensions an exact Jacobian formula for invertible Lüders updates gives a volume-contraction criterion. Spacelike vacuum correlations and strict CHSH violations persist throughout sufficiently small observational parcels. Reeh--Schlieder cyclicity becomes finite-precision local reachability, while parcel equivalence of vacuum refinements implies vacuum GNS equivalence and hence does not evade Haag-type obstructions. Tomita--Takesaki modular automorphisms act on parcels, measurement update is modularly covariant, and modular conjugation induces a duality between normal parcels of an algebra and its commutant. State-dependent modular correlations are continuous under predual-norm variation of faithful normal states; shrinking parcels with vanishing KMS defect recover a KMS state. Bisognano--Wichmann yields a parcel formulation of the Unruh effect, recovering the exact KMS relation and Unruh temperature under refinement. Finally, limiting projection faces and their conjugation actions recover the Murray--von Neumann factor classification.
CommentsIn this version, the paper has been shortened and polished by removing repetitive material while retaining the results and proofs. A subtitle has been added to make the title more informative. The previously introduced Spectral Regularity Axiom has been removed, since the revised relative-modular continuity argument shows that no such additional spectral assumption is required
