量子化作为一种降维现象
Quantization as a dimensional reduction phenomenon
摘要：
经典力学，在库普曼和冯诺依曼的运算公式中，也可以写成函数形式。在这种形式中，时间的两个格拉斯曼伙伴使它们的自然外观以这种方式将时间延伸到三维的超流形。量子化，然后实现了一个过程中的降维这个supermanifold。我们证明了这一过程是等价于众所周知的几何量子化的方法。
英文摘要：
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three dimensional supermanifold. Quantization is then achieved by a process of dimensional reduction of this supermanifold. We prove that this procedure is equivalent to the well-known method of geometric quantization.
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