量子过程与能量动量流
Quantum Processes and Energy-Momentum Flow
摘要：
在本文中，我们专注于简单量子系统中的能量流。这是通过专注于量子哈密顿-雅可比方程来实现的。我们展示了这个方程如何以三种不同但相关的方式出现在标准量子形式主义中，从标准薛定谔方程，从拉格朗日场论和从冯诺依曼-莫亚尔代数。这个方程允许我们使用能量-动量张量来跟踪能量流，其中的分量与四动量算子的弱值有关。这开辟了一条新的途径来探索这些组件的经验。代数方法使我们能够讨论潜在的非交换辛几何的物理意义，提出量子系统中粒子结构的问题。
英文摘要：
In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different but related ways, from the standard Schrödingier equation, from Lagrangian field theory and from the von Neumann-Moyal algebra. This equation allows us to track the energy flow using the energy-momentum tensor, the components of which are related to weak values of the four-momentum operator. This opens up a new way to explore these components empirically. The algebraic approach enables us to discuss the physical significance of the underlying non-commutative symplectic geometry, raising questions as to the structure of particles in quantum systems.
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