阿贝尔规范理论环变换的归纳构造
Inductive Construction of the Loop Transform for Abelian Gauge Theories
摘要：
在阿贝尔规范理论的情况下，我们构造了环变换作为由环面上傅里叶变换的归纳极限给出的幺正算符。我们还证明了它的值域，即量子圈表象的运动学态空间，是圈群上平方可积复值函数的Hilbert空间。
英文摘要：
We construct the loop transform in the case of Abelian gauge theories as unitary operator given by the inductive limit of Fourier transforms on tori. We also show that its range, i.e.the space of kinematical states of the quantum loop representation, is the Hilbert space of square integrable complex valued functions on the group of loops.
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