CAUSAL EVOLUTION OF SPIN NETWORKS

A new approach to quantum gravity is described which joins the loop re presentation formulation of the canonical theory to the causal set for mulation of the path integral. The theory assigns quantum amplitudes t o special classes of causal sets, which consist of spin networks repre senting quantum states of the gravitational field joined together by l abeled null edges, The theory exists in 3 + 1-, 2 + 1- and 1 + 1-dimen sional versions, and may also be interpreted as a theory of labeled ti melike surfaces. The dynamics is specified by a choice of functions of the labelings of d + 1-dimensional simplices, which represent element ary future light cones of events in these discrete space-times. The qu antum dynamics thus respects the discrete causal structure of the caus al sets. In the 1 + 1-dimensional case the theory is closely related t o directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation,leading to the exis tence of a classical limit. (C) 1997 Published by Elsevier Science B.V .