量子场论中贝尔不等式的范畴论视角
A categorical view of Bell's inequalities in quantum field theory
AI总结：
本文将贝尔不等式从代数量子场论推广到局部协变量子场论，利用态空间的函子化表述证明CHSH不等式在容许四元组构成的态范畴中成立，并在代数态射和时空等距嵌入下保持不变。
摘要：
我们提出将代数量子场论（AQFT）中对贝尔不等式的描述推广到局部协变量子场论（LCQFT）的语境中。我们利用奠基性工作\cite{BFV03}中提出的态空间的函子化表述来证明，对于由所有可能的容许四元组构成的合适子范畴，会产生一个关于此类可观测量的态范畴，该范畴满足Clauser-Horne-Shimony-Holt（CHSH）不等式。该不等式在代数态射下被平凡地保持，并且态空间的函子性向我们保证，它在定义代数的全局双曲时空之间的等距嵌入下也被保持，这些时空构成了局部协变QFT函子。
英文摘要：
We propose a generalization of the description of Bell's inequalities in algebraic quantum field theory (AQFT) to the context of locally covariant quantum field theory (LCQFT). We use the functorial formulation of the state space as proposed in the seminal work \cite{BFV03} to show that for the suitable subcategory which consists of all possible admissible quadruples, yields a category of states over such observables which satisfy the Clauser-Horne-Shimony-Holt (CHSH) inequality. Such inequality is trivially preserved under algebraic morphisms and functoriality of the state space asserts us that it is preserved under isometric embeddings between the globally hyperbolic spacetimes where the algebras are defined and which constitute the locally covariant QFT functor.
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