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arXiv · 1309.2187

Theory of intersecting loops on a torus

J. E. Nelson·R. F. Picken
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Abstract

We continue our investigation into intersections of closed paths on a torus, to further our understanding of the commutator algebra of Wilson loop observables in 2+1 quantum gravity, when the cosmological constant is negative. We give a concise review of previous results, e.g. that signed area phases relate observables assigned to homotopic loops, and present new developments in this theory of intersecting loops on a torus. We state precise rules to be applied at intersections of both straight and crooked/rerouted paths in the covering space $\mathbb{R}^2$. Two concrete examples of combinations of different rules are presented.

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J. E. Nelson, R. F. Picken. 2014-04-10. Theory of intersecting loops on a torus. https://arxiv.org/abs/1309.2187

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