Maslov指数、Poisson括号和奇异微分形式
Maslov indices, Poisson brackets, and singular differential forms
摘要：
Maslov指数是出现在半经典波函数和量子化条件中的整数。它们通常是出了名的难以计算。我们提出的方法计算的Maslov指数，只依赖于典型的初等泊松括号和简单的线性代数。我们还提出了一个奇异的微分形式，其沿曲线的积分给出了该曲线的Maslov指数。该形式是封闭的，但不是精确的，并且在正则变换下通过精确微分变换。我们用$6j$ -符号来说明这个方法，这个符号在角动量理论和量子引力中很重要。
英文摘要：
Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the $6j$-symbol, which is important in angular momentum theory and in quantum gravity.
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