Hall相干态、Cameron-Martin定理和Yang-Mills理论在圆上的量子化
Hall's coherent states, the Cameron-Martin theorem, and the quantization of Yang-Mills theory on a circle
摘要：
本文讨论了圆上的杨-米尔斯理论的物理自由度空间的经典和量子化约化（使得时空是圆柱体）。虽然经典的约化相空间是有限维的，但量子约化过程在数学上是迷人的，首先涉及循环群上的维纳测度，其次是将Cameron-Martin定理推广到循环群，第三是紧致李群的Hall相干态。我们的方法是基于量子模拟的经典Marsden-Weinstein辛约化过程。
英文摘要：
We discuss the classical and quantum reduction to the space of physical degrees of freedom of Yang--Mills theory on a circle (so that space-time is a cylinder). Although the classical reduced phase space is finite-dimensional, the quantum reduction procedure is mathematically fascinating, involving firstly the Wiener measure on a loop group, secondly a generalization of the Cameron--Martin theorem to loop groups, and thirdly Hall's coherent states for compact Lie groups. Our approach is based on a quantum analogue of the classical Marsden--Weinstein symplectic reduction process.
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