标题： 正则变量的去耦与Koopman-von Neumann理论 显示英文标题

标题： Deconjugation of canonical variables and the Koopman-von Neumann theory

摘要： Koopman-von Neumann（KvN）理论是一种动力学动量与位置不是共轭的理论，即位置和动量被解耦。 从这个角度来看，我们展示了KvN理论源于量子力学，并从中提取出经典的运动方程。 然而，保留该理论的规范结构需要引入“辅助”的位置和动量共轭变量。 我们表明，使用KvN形式化来研究量子和经典系统之间的相互作用会使辅助变量承担物理角色。 尽管它表现出经典行为，但KvN理论可能不仅仅局限于经典范畴。 显示英文摘要

摘要： The Koopman-von Neumann (KvN) theory is one where the dynamical momentum is not canonically conjugate to position, i.e., position and momentum are deconjugated. From this point of view, we show that the KvN theory arises from quantum mechanics, extracting classical equations of motion from quantum ones. However, preserving the canonical structure of the theory requires introducing ``auxiliary'' canonical conjugates to position and momentum. We show that using the KvN formulation to study the interaction between quantum and classical systems forces the auxiliary variables to take on a physical role. While giving rise to classical behaviour, the KvN theory might be more than classical.