arXiv 1007.46152010-07gr-qchep-thmath-phmath.MP

Combinatorial quantisation of the Euclidean torus universe

C. Meusburger, K. Noui

备注：: 47 pages, 2 eps figures, minor changes, typos corrected
发表信息：: Nucl.Phys.B841:463-505,2010
DOI：: 10.1016/j.nuclphysb.2010.08.014

英文摘要：

We quantise the Euclidean torus universe via a combinatorial quantisation formalism based on its formulation as a Chern-Simons gauge theory and on the representation theory of the Drinfel'd double DSU(2). The resulting quantum algebra of observables is given by two commuting copies of the Heisenberg algebra, and the associated Hilbert space can be identified with the space of square integrable functions on the torus. We show that this Hilbert space carries a unitary representation of the modular group and discuss the role of modular invariance in the theory. We derive the classical limit of the theory and relate the quantum observables to the geometry of the torus universe.

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