Constant connections, quantum holonomies and the Goldman bracket

Details Constant connections, quantum holonomies and the Goldman bracket Constant connections, quantum holonomies and the Goldman bracket

2004-12-02

arxiv.org/abs/math-ph/0412007v3

Adv.Theor.Math.Phys. 9 (2005) 407-433

Physics

Mathematical Physics

25 pages, 43 figures, using ATMP style file, to appear Adv.Theor.Math.Phys. Vol 9 (2005)

Scientific paper

In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x 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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