Open Access
June 2014 Theory of intersecting loops on a torus
J. E. Nelson, R. F. Picken
Adv. Theor. Math. Phys. 18(3): 709-740 (June 2014).


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. "Theory of intersecting loops on a torus." Adv. Theor. Math. Phys. 18 (3) 709 - 740, June 2014.


Published: June 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1306.53009
MathSciNet: MR3274793

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 3 • June 2014
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