代数量子场论中的波前集
Wavefront sets in algebraic quantum field theory
摘要：
弯曲时空中量子场论的微定域分析概念所得到的结果，使量子场论中n点分布的波前集的研究最近引起了人们的注意。本文推广了分布波前集的概念，使之适用于任意维平移群协变作用的算子代数网上的状态和线性泛函。在算子代数框架下给出量子场论的情况下，进一步研究了波前集的广义概念，称之为“渐近相关谱”，并导出了它在物理状态下的若干性质。我们还调查了渐近相关谱的物理状态和相应的Wightman分布的波前集之间的连接，如果有一个Wightman场隶属于本地运营商代数。最后，我们提出了一个新的结果（推广已知的事实），这表明，某些时空点必须包含在奇异的支持的2n点分布的非平凡的Wightman场。
英文摘要：
The investigation of wavefront sets of n-point distributions in quantum field theory has recently acquired some attention stimulated by results obtained with the help of concepts from microlocal analysis in quantum field theory in curved spacetime. In the present paper, the notion of wavefront set of a distribution is generalized so as to be applicable to states and linear functionals on nets of operator algebras carrying a covariant action of the translation group in arbitrary dimension. In the case where one is given a quantum field theory in the operator algebraic framework, this generalized notion of wavefront set, called "asymptotic correlation spectrum", is further investigated and several of its properties for physical states are derived. We also investigate the connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding Wightman distributions if there is a Wightman field affiliated to the local operator algebras. Finally we present a new result (generalizing known facts) which shows that certain spacetime points must be contained in the singular supports of the 2n-point distributions of a non-trivial Wightman field.
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