Relativistic Spin Networks and Quantum Gravity

Abstract

. Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) \\Theta SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geometry of the edges of a 3-simplex. This leads us to suggest that there may be a 4-dimensional state sum model for quantum gravity based on relativistic spin networks which parallels the construction of 3-dimensional quantum gravity from ordinary spin networks. PACS 04.60.Nc. Typeset by A M S-T E X 2 JOHN W. BARRETT LOUIS CRANE I. Introduction In [1] and [2], it was proposed that the quantum theory of gravity could take the form of a very special type of discrete model on a triangulated 4-manifold, which has the property that the propagation of physical states does not depend on the choice of triangulation. Such a model is called a topological state sum. Topological state sums are closely relat...