论文标题
转移操作员的相对论量子波函数的方法
A Transfer Operator Approach to Relativistic Quantum Wavefunction
论文作者
论文摘要
Koopman-Von Neumann形式主义的最初意图是通过将操作员形式主义引入古典力学，将经典和量子力学置于同一基础上。在这里，我们以相反的方式追求他们的路径，并检查转移操作员对量子机械演变的评价。为此，我们在4维伪里程歧管上引入了一个具有物理动机的标量波形形式主义，并为速度场引入了速度场，并获得了相关波函数的进化方程，这是相关的加权转移操作员的生成器。标量演化的发电机在时空和时间上是一阶。形式主义的概率解释导致在非相关性极限中恢复Schr Odinger方程。在特殊的相对性限制中，我们表明Dirac Spinors的标量波函数满足新方程。提供了与质量的弦理论考虑的连接。
The original intent of the Koopman-von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanics. Here we pursue their path the opposite way and examine what transfer operators can say about quantum mechanical evolution. To that end, we introduce a physically motivated scalar wavefunction formalism for a velocity field on a 4-dimensional pseudo-Riemannian manifold, and obtain an evolution equation for the associated wavefunction, a generator for an associated weighted transfer operator. The generator of the scalar evolution is of first order in space and time. The probability interpretation of the formalism leads to recovery of the Schrodinger equation in the non-relativistic limit. In the special relativity limit, we show that the scalar wavefunction of Dirac spinors satisfies the new equation. A connection with string theoretic considerations for mass is provided.
