Determination and Reduction of Large Diffeomorphisms

We shall consider diffeomorphism invariant theories within the Hamiltonian formulation, where space-time is assumed to be a topological product M ∼= Σ × R. The constraints of the theory will only generate the identity component D(Σ) of some subgroup D(Σ) of diffeomorphisms of Σ. This means that after a reduction by D(Σ), i.e., implementing the constraints – which itself is a highly non-trivial problem –, one still has a residual action of the discrete and generally non-abelian and infinite group