论文标题
束理论描述了大规模的单粒子状态空间；朝着相对论量子信息理论的看法
Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory
论文作者
论文摘要
相对论量子信息理论（RQI）是物理学蓬勃发展的研究领域，但是该领域没有系统的数学处理。在本文中，我们建议对大量单粒子状态空间的理论描述，这些空间是RQI的基本构件。用束理论的语言，可以在巨大粒子的所有可能运动状态的集合上构造矢量束，其中将其纤维纤维编码为固定惯性观察者所感知的移动粒子的内部量子状态。通常的希尔伯特空间描述之间的链接是由捆绑包的$ l^2 $ section Space上的广义感应的表示构造提供的。本文的目的是两个方面。一种是将RQI的基本思想传达给数学家，另一个是为单粒子状态空间提出改进的形式，其中包含所有已知的巨大粒子，包括在RQI文献中从未处理过的粒子。在本文的最后，将探讨形式主义的一些理论含义。
Relativistic Quantum Information Theory (RQI) is a flourishing research area of physics, yet, there has been no systematic mathematical treatment of the field. In this paper, we suggest bundle theoretic descriptions of massive single-particle state spaces, which are basic building blocks of RQI. In the language of bundle theory, one can construct a vector bundle over the set of all possible motion states of a massive particle, in whose fibers the moving particle's internal quantum state as perceived by a fixed inertial observer is encoded. A link between the usual Hilbert space description is provided by a generalized induced representation construction on the $L^2$-section space of the bundle. The aim of this paper is two-fold. One is to communicate the basic ideas of RQI to mathematicians and the other is to suggest an improved formalism for single-particle state spaces that encompasses all known massive particles including those which have never been dealt with in the RQI literature. Some of the theoretical implications of the formalism will be explored at the end of the paper.
