自同构群的连续谱与粒子问题
Continuous Spectrum of Automorphism Groups and the Infraparticle Problem
摘要：
本文给出了Banach空间上一组等距映射的精细谱分析的一般框架，推广了Arveson的谱理论。引入了连续Arveson谱的概念，定义了相应的谱子空间.该谱的绝对连续和奇异连续部分被指定。条件给出，在转置的作用组的等距，这保证了纯点和连续子空间跨越整个Banach空间。在作用于$C^*$ -代数上的酉实现自同构群的情况下，找到了自同构的连续谱与实现酉群的谱之间的关系，并对量子场论中的时空平移自同构群进行了详细的分析.特别是，它表明，其连续谱的结构是相关的（红外）粒子在给定的理论存在的问题。
英文摘要：
This paper presents a general framework for a refined spectral analysis of a group of isometries acting on a Banach space, which extends the spectral theory of Arveson. The concept of continuous Arveson spectrum is introduced and the corresponding spectral subspace is defined. The absolutely continuous and singular-continuous parts of this spectrum are specified. Conditions are given, in terms of the transposed action of the group of isometries, which guarantee that the pure-point and continuous subspaces span the entire Banach space. In the case of a unitarily implemented group of automorphisms, acting on a $C^*$-algebra, relations between the continuous spectrum of the automorphisms and the spectrum of the implementing group of unitaries are found. The group of spacetime translation automorphisms in quantum field theory is analyzed in detail. In particular, it is shown that the structure of its continuous spectrum is relevant to the problem of existence of (infra-)particles in a given theory.
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