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arXiv · 1806.09262

Revisiting Quantum Volume Operator

Leonid Perlov
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Abstract

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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Leonid Perlov. 2018-06-25. Revisiting Quantum Volume Operator. https://arxiv.org/abs/1806.09262

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