QUANTUM GEOMETRY WITH INTRINSIC LOCAL CAUSALITY - ART. NO. 084032

The space of states and operators for a large class of background inde pendent theories of quantum spacetime dynamics is defined. The SU(2) s pin networks of quantum general relativity are replaced by labelled co mpact two-dimensional surfaces. The space of states of the theory is t he direct sum of the spaces of invariant tensors of a quantum group G( q) over all compact (finite genus) oriented 2-surfaces. The dynamics i s background independent and locally causal. The dynamics constructs h istories with discrete features of spacetime geometry such as causal s tructure and multifingered time. For SU(2) the theory satisfies the Be kenstein bound and the holographic hypothesis is recast in this formal ism. [S0556-2821(98)04320-3].