We analyze the quantization of a system consisting of a particle in an external Yang–Mills field within a C*-algebraic framework. We show that in both the classical and quantum theories of such a system, the kinematical algebra of physical quantities can be obtained by restricting attention to symmetry-invariant states on a C*-algebra. We use this to show that symmetry-invariant quantum states correspond to symmetry-invariant classical states in the classical limit.

中文翻译：

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规范不变态的经典极限和严格量化的代数选择

我们分析了一个系统的量化，该系统由一个 C*-代数框架内的外部杨-米尔斯场中的粒子组成。我们表明，在这种系统的经典理论和量子理论中，可以通过将注意力限制在 C*-代数上的对称不变状态来获得物理量的运动代数。我们用它来证明对称不变的量子态对应于经典极限中的对称不变的经典态。