Time evolution of Hamiltonian constraint system: an idea applicable to quantum gravity

Abstract

The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other observables evolve. We study if it plays the role of time. As simple examples, we study the theories of non-relativistic and relativistic particles. We outline an application of the idea to general relativity.