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Constant connections, quantum holonomies and the Goldman bracket

J. E. Nelson·R. F. Picken
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Abstract

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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J. E. Nelson, R. F. Picken. 2005-10-03. Constant connections, quantum holonomies and the Goldman bracket. https://arxiv.org/abs/math-ph/0412007

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