Combinatorial space from loop quantum gravity

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  • 14 March 1997
Abstract
In loop quantum gravity smoothly embeded loops are not enough to provide a quantum representation of the loop algebra. Since the space of smooth loops must be `enlarged' to include loops with intersections, the quantum symmetry group has to be `enlarged' accordingly. After considering the complete quantum symmetry group, the space of `diffeomorphism' invariant states is reconstructed simplifying two troublesome issues of previous formulations. First, the needed background structure is much weaker and one can show that different choices of background yield equivalent quantum theories. Second, the space of `diffeomorphism' invariant states is separable (the s-knot basis is countable) in contrast with the previous constructions.

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