零局部模流的唯一性
Uniqueness of null-local modular flow
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中文总结 AI 辅助
研究零局部模流的唯一性问题，通过研究无质量克莱因 - 戈登理论，为因果菱形过去零边界矢量场构造态，经计算表明此类态在同一局部希尔伯特空间唯一，还论证了真空扇区零局部模流由真空态提供，并对其他情况进行评论。
中文摘要 AI 辅助
在arXiv:2306.01837中，有人推测可以设计出一大类量子场论态，使得类空切片上的模流是“瞬时局部的”。本文表明，在零切片上，此类流受到高度限制；紫外通用性本质上要求零局部模流是唯一的。具体而言，我们研究了闵可夫斯基时空中的无质量克莱因 - 戈登理论，为因果菱形过去零边界上任何足够正则的未来定向矢量场构造了一个以该矢量场为其瞬时模流的态。然后通过显式计算表明，该类中不存在两个不同的态能在同一局部希尔伯特空间中实现。通过更抽象的论证，我们还表明在该理论的真空扇区中，因果菱形中唯一的零局部模流由真空态本身提供。我们还对有质量标量、自由麦克斯韦场、自由引力子以及弯曲背景下的零局部模流构造进行了评论。
英文摘要
In arXiv:2306.01837, it was conjectured that one can engineer a large class of quantum field theory states for which the modular flow on a spacelike slice is "instantaneously local." Here we show that on null slices, such flows are highly constrained; ultraviolet universality essentially requires null-local modular flow to be unique. Concretely, we study massless Klein-Gordon theory in Minkowski spacetime, and construct, for any sufficiently regular future-directed vector field on the past null boundary of a causal diamond, a state that has this vector field as its instantaneous modular flow. We then show by explicit computation that no two distinct states in this class can be realized in the same local Hilbert space. Using a more abstract argument, we also show that in the vacuum sector of the theory, the only null-local modular flow in a causal diamond is provided by the vacuum state itself. We also comment on the construction of null-local modular flow for massive scalars, free Maxwell fields, free gravitons, and in curved backgrounds.
