再论量子体积算符
Revisiting Quantum Volume Operator
摘要：
本文利用n维完整变分公式引入了n维超曲面量子体积算符。在三维情况下，我们直接引入n维体积算子，而不是用n-1维超曲面体积算子构造n维超曲面体积算子.我们使用两个事实-第一，n+1维流形的n维超曲面的面积是n维诱导度量的体积，第二，holonomy变分公式对n+1维流形中的n维超曲面有效，其连接值在任何李代数中。
英文摘要：
In this paper we introduce the n-dimensional hypersurface quantum volume operator by using the n-dimensional holonomy variation formula. Instead of trying to construct the n-dimensional hypersurface volume operator by using the n-1 dimensional hypersufrace volume operators, as it is usually done in 3d case, we introduce the n-dimensional volume operator directly. We use two facts - first, that the area of the n-dimensional hypersurface of the n+1 dimensional manifold is the volume of the n dimensional induced metric and secondly that the holonomy variation formula is valid for the n-dimensional hypersufrace in the n+1 manifold with connection values in any Lie algebra.
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