标题： 无时间量子理论中的幺正性条件 显示英文标题

标题： Conditions for Unitarity in Timeless Quantum Theory

摘要： 量子无时间方法通过在静态量子宇宙中相对于时钟恢复量子理论的通常幺正演化来解决时间问题。 对于某些宇宙的哈密顿量，例如包含与时钟相互作用项的哈密顿量，动力学特性会发生显著变化，可能是非幺正的。 这项工作推导了相对动力学为幺正的必要且充分条件，并找到了幺正演化算子的一般形式。 这些条件的物理解释是基于时钟的速率。 幺正动力学与随时间恒定且独立于时钟内部结构的速率相关。 显示英文摘要

摘要： Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an interaction term with the clock, the dynamics is substantially altered and can be non-unitary. This work derives necessary and sufficient conditions for the relative dynamics to be unitary and finds the general form of the unitary evolution operator. A physical interpretation of these conditions is given in terms of the clock's rate. Unitary dynamics is associated with rates that are constant in time and independent of the clock's internal structure.