2D manifold-independent spinfoam theory

Details 2D manifold-independent spinfoam theory 2D manifold-independent spinfoam theory

Oct 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003cqgra..20.4425l&link_type=abstract

Classical and Quantum Gravity, Volume 20, Issue 20, pp. 4425-4445 (2003).

Mathematics

Logic

6

Scientific paper

A number of background-independent quantization procedures have recently been employed in 4D nonperturbative quantum gravity. We investigate and illustrate these techniques and their relation in the context of a simple 2D topological theory. We discuss canonical quantization, loop or spin network states, path integral quantization over a discretization of the manifold, spin foam formulation and the fully background-independent definition of the theory using an auxiliary field theory on a group manifold. While several of these techniques have already been applied to this theory by Witten, the last one is novel: it allows us to give a precise meaning to the sum over topologies, and to compute background-independent and, in fact, 'manifold-independent' transition amplitudes. These transition amplitudes play the role of Wightman functions of the theory. They are physical observable quantities, and the canonical structure of the theory can be reconstructed from them via a Cast algebraic GNS construction. We expect an analogous structure to be relevant in 4D quantum gravity.

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