Relativistic spin networks and quantum gravity

Relativistic spin networks are defined by considering the spin covering of the group SO(4), $\mathrm{SU(2)\times SU(2)}.$ Relativistic quantum spins are related to the geometry of the two-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 four-dimensional state sum model for quantum gravity based on relativistic spin networks that parallels the construction of three-dimensional quantum gravity from ordinary spin networks.