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Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
Buffenoir, E. ; Noui, K. ; Roche, P.
HAL, hal-00178161 / Harvested from HAL
We analyze the hamiltonian quantization of Chern-Simons theory associated to the universal covering of the Lorentz group SO(3,1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological surface. Our main result is a construction of a unitary representation of this algebra. For this purpose, we use the formalism of combinatorial quantization of Chern-Simons theory, i.e we quantize the algebra of polynomial functions on the space of flat SL(2,C)-connections on a topological surface with punctures. This algebra admits a unitary representation acting on an Hilbert space which consists in wave packets of spin-networks associated to principal unitary representations of the quantum Lorentz group. This representation is constructed using only Clebsch-Gordan decomposition of a tensor product of a finite dimensional representation with a principal unitary representation. The proof of unitarity of this representation is non trivial and is a consequence of properties of intertwiners which are studied in depth. We analyze the relationship between the insertion of a puncture colored with a principal representation and the presence of a world-line of a massive spinning particle in de Sitter space.
Publié le : 2002-07-05
Classification:  PACS: 0460K, 0220U,  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],  [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc],  [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00178161,
     author = {Buffenoir, E. and Noui, K. and Roche, P.},
     title = {Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00178161}
}
Buffenoir, E.; Noui, K.; Roche, P. Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00178161/