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June 2005 Constant connections, quantum holonomies and the Goldman bracket
J. E. Nelson, R. F. Picken
Adv. Theor. Math. Phys. 9(3): 407-433 (June 2005).


In the context of $2+1$-dimensional quantum gravity with negative cosmological constant and topology $\mathbb{R} \times T^2$, constant matrix-valued connections generate a $q$-deformed representation of the fundamental group, and signed area phases relate the quantum matrices assigned to homotopic loops. Some features of the resulting quantum geometry are explored, and as a consequence a quantum version of the Goldman bracket is obtained.


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J. E. Nelson. R. F. Picken. "Constant connections, quantum holonomies and the Goldman bracket." Adv. Theor. Math. Phys. 9 (3) 407 - 433, June 2005.


Published: June 2005
First available in Project Euclid: 3 April 2006

zbMATH: 1158.83018
MathSciNet: MR2201681

Rights: Copyright © 2005 International Press of Boston

Vol.9 • No. 3 • June 2005
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