论文标题
N颗粒的相对论量子力学的欧几里得公式
Euclidean formulation of relativistic quantum mechanics of N particles
论文作者
论文摘要
讨论了一种相对论量子力学的欧几里得公式，以有限数量的自由度。需要对量子理论的相对论治疗来研究亚音线距离尺度上的HADRONIC系统。尽管事实证明，相对论量子力学的直接相互作用方法很有用，但它们有两个缺点。一个是，对于两个以上粒子的系统，很难实现群集特性。第二个是与量子场理论的关系是间接的。相对论量子力学的欧几里得公式提供了没有这些困难的替代表示。更令人惊讶的是，该理论可以完全在欧几里得代表中提出，而无需进行分析延续。在这项工作中，讨论了相对论$ n $粒子系统的欧几里得表示。给出了任何自旋的n个自由颗粒系统的内核，并显示为反射阳性。构建了庞加莱群的发电机的明确公式，并在希尔伯特空间的欧几里得代表中构建了自旋的旋转公式。讨论了保留欧几里得协方差和反思阳性的相关结构。
A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. While direct interaction approaches to relativistic quantum mechanics have proved to be useful, they have two disadvantages. One is that cluster properties are difficult to realize for systems of more than two particles. The second is that the relation to quantum field theories is indirect. Euclidean formulations of relativistic quantum mechanics provide an alternative representation that does not have these difficulties. More surprising, the theory can be formulated entirely in the Euclidean representation without the need for analytic continuation. In this work a Euclidean representation of a relativistic $N$-particle system is discussed. Kernels for systems of N free particles of any spin are given and shown to be reflection positive. Explicit formulas for generators of the Poincaré group for any spin are constructed and shown to be self-adjoint on the Euclidean representation of the Hilbert space. The structure of correlations that preserve both the Euclidean covariance and reflection positivity is discussed.
