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arXiv 2009.12342hep-thgr-qcmath-phmath.MP
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量子场论中的定域性和广义定域性

Locality and General Vacua in Quantum Field Theory

Daniele Colosi, Robert Oeckl

摘要:

我们扩展了一般边界量子场论(GBQFT)的框架,实现了对现实量子场论的完全局域描述。这就需要对非凯勒极化进行量子化,而这些非凯勒极化一般都发生在洛伦兹时空的类时超曲面上,正如最近已经证明的那样。我们通过两种方式实现这一点:一方面,我们用超曲面上的可观测量取代希尔伯特空间态,这是基于代数量子场论的精神。另一方面,我们将GNS构造应用于扭曲星结构以获得Hilbert空间,其动机是量子场论的欧几里得方法的反射正性概念。结果之一是,真空态在另一个真空的希尔伯特空间中用大量粒子对表示的著名表示,允许对非凯勒真空进行广泛的推广,特别是在类时超曲面上。

英文摘要:

We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations which occur generically on timelike hypersurfaces in Lorentzian spacetimes as has been shown recently. We achieve this in two ways: On the one hand we replace Hilbert space states by observables localized on hypersurfaces, in the spirit of algebraic quantum field theory. On the other hand we apply the GNS construction to twisted star-structures to obtain Hilbert spaces, motivated by the notion of reflection positivity of the Euclidean approach to quantum field theory. As one consequence, the well-known representation of a vacuum state in terms of a sea of particle pairs in the Hilbert space of another vacuum admits a vast generalization to non-Kähler vacua, particularly relevant on timelike hypersurfaces.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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