Combinatorial quantisation of the Euclidean torus universe

Meusburger C, Noui K (2010)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2010

Journal

Nuclear Physics B Elsevier

Publisher: Elsevier

Book Volume: 841

Pages Range: 463-505

Journal Issue: 3

DOI: 10.1016/j.nuclphysb.2010.08.014

Abstract

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. © 2010 Elsevier B.V.

Authors with CRIS profile

Cathérine Meusburger Professur für Mathematik (Darstellungstheorie und Mathematische Physik)

Involved external institutions

François Rabelais University Tours FR France (FR)

How to cite

APA:

Meusburger, C., & Noui, K. (2010). Combinatorial quantisation of the Euclidean torus universe. Nuclear Physics B, 841(3), 463-505. https://dx.doi.org/10.1016/j.nuclphysb.2010.08.014

MLA:

Meusburger, Cathérine, and Karim Noui. "Combinatorial quantisation of the Euclidean torus universe." Nuclear Physics B 841.3 (2010): 463-505.

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