标题： 时空密度矩阵：形式与性质 显示英文标题

标题： Spacetime Density Matrix: Formalism and Properties

摘要： 在本文中，我们发展了时空密度矩阵的一般形式和性质，该矩阵捕捉了不同柯西面上的相关性，可以被视为定义在单个柯西面上的标准密度矩阵的自然推广。 我们给出了一般量子系统中时空密度矩阵的构造及其通过施温格-凯尔迪什路径积分的表示。 我们进一步引入了一个超算符框架，在该框架中，时空密度矩阵作为一个特例出现，并从这一角度讨论了可能的推广。 我们还表明，时空密度矩阵满足一种类似刘维尔-冯诺依曼类型的运动方程。 在考虑子系统时，可以通过对互补自由度进行迹运算来定义约化的时空密度矩阵。 我们研究了其矩的一般性质，并特别推导了二阶矩的普遍短时间行为。 我们发现，子系统之间的耦合在获得非平凡结果中起着关键作用。 假设弱耦合，我们开发了一种微扰方法来系统地计算这些矩。 显示英文摘要

摘要： In this paper, we develop the general formalism and properties of the spacetime density matrix, which captures correlations among different Cauchy surfaces and can be regarded as a natural generalization of the standard density matrix defined on a single Cauchy surface. We present the construction of the spacetime density matrix in general quantum systems and its representation via the Schwinger Keldysh path integral. We further introduce a super-operator framework, within which the spacetime density matrix appears as a special case, and discuss possible generalizations from this perspective. We also show that the spacetime density matrix satisfies a Liouville von Neumann type equation of motion. When considering subsystems, a reduced spacetime density matrix can be defined by tracing over complementary degrees of freedom. We study the general properties of its moments and, in particular, derive universal short time behavior of the second moment. We find that coupling between subsystems plays a crucial role in obtaining nontrivial results. Assuming weak coupling, we develop a perturbative method to compute the moments systematically.