Theory of intersecting loops on a torus
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 . Two concrete examples of combinations of different rules are presented.
Cite
@article{arxiv.1309.2187,
title = {Theory of intersecting loops on a torus},
author = {J. E. Nelson and R. F. Picken},
journal= {arXiv preprint arXiv:1309.2187},
year = {2014}
}
Comments
31 pages, 30 figures. Version 2 has an improved text for the abstract. To appear in Adv. Theor. Math. Phys., Issue 18.3, May-June 2014. arXiv admin note: text overlap with arXiv:1006.0921