Quasilocal energy for spin-net gravity

Abstract

The Hamiltonian of the gravitational field defined in a bounded region is quantized. The classical Hamiltonian, and starting point for the regularization, is a boundary term required by functional differentiability of the Hamiltonian constraint. It is the quasilocal energy of the system and becomes the ADM mass in asymptopia. The quantization is carried out within the framework of canonical quantization using spin networks. The result is a gauge-invariant, well-defined operator on the Hilbert space induced by the state space on the whole spatial manifold. The spectrum is computed. An alternative form of the operator, with the correct naive classical limit, but requiring a restriction on the Hilbert space, is also defined. Comparison with earlier work and several consequences are briefly explored.