Hamiltonian quantization of Chern-Simons theory with SL(2, Bbb C) group

Classical and Quantum Gravity (Impact Factor: 3.56). 01/2002; 19(19):4953-5015. DOI: 10.1088/0264-9381/19/19/313
Source: arXiv

ABSTRACT We analyse the Hamiltonian quantization of Chern-Simons theory associated with the real group SL(2, Sigma with punctures. This algebra, the so-called moduli algebra, is constructed along the lines of Fock-Rosly, Alekseev-Grosse-Schomerus, Buffenoir-Roche using only finite-dimensional representations of Uq(sl(2, Bbb C)Bbb R). It is shown that this algebra admits a unitary representation acting on a Hilbert space which consists of wave packets of spin networks associated with principal unitary representations of Uq(sl(2, Bbb C)Bbb R). The representation of the moduli algebra is constructed using only Clebsch-Gordan decomposition of a tensor product of a finite-dimensional representation with a principal unitary representation of Uq(sl(2, Bbb C)Bbb R). The proof of unitarity of this representation is nontrivial and is a consequence of the properties of Uq(sl(2, Bbb C)Bbb R) intertwiners which are studied in depth. We analyse the relationship between the insertion of a puncture coloured with a principal representation and the presence of a worldline of a massive spinning particle in de Sitter space.

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