A note on the Hamiltonian constraint in canonical GR

Abstract

The Hamiltonian constraint of the coupled Einstein-Yang-Mills-Higgs system with a cosmological constant is shown to be a pure Poisson bracket of a dimensionless functional on the phase space and the volume of the three-space. One of its potential consequences, a restriction on the eigenstates of the volume operator in a class of canonical quantum gravity theories, is also pointed out.