hamiltonian formulation of scalar density field theory

In the adm formalism, spacetime is foliated by spacelike hypersurfaces, dividing spacetime into spaceand time. in this formalism, the evolution of fields can be separated into evolution on thesehypersurfaces and evolution from one hypersurface to the next. teitelboim showed that by solving thealgebra of the generators under certain assumptions, the hamiltonian of scalar field, maxwell's field,and general relativity can be obtained[1]. in this paper, we solve this algebra for scalar density field theory in arbitrary curved spacetime and demonstrate that scalar density fields with weights zero and one are permissible within the hamiltonian formalism.