Some results of SU(2) spinorial lattice gravity

Abstract

The author reports on the status of the closure problem for the regularised constraint operators of general relativity within the SU(2) spinorial Hamiltonian lattice gauge theory framework constructed in a previous work. The author describes how the diffeomorphism subalgebra is recovered upon removal of the regulator. Comparisons are drawn with the work of Rovelli and Smolin (1988) in the continuum, and it is described how the lattice framework provides a natural analogue of the sector of the physical state space that they describe.