Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra
arXiv:gr-qc/9601043 · doi:10.1088/0264-9381/13/11/022
Abstract
We discuss the issue initiated by Kuchař {\it et al}, of replacing the usual Hamiltonian constraint by alternative combinations of the gravitational constraints (scalar densities of arbitrary weight), whose Poisson brackets strongly vanish and cast the standard constraint-system for vacuum gravity into a form that generates a true Lie algebra. It is shown that any such combination---that satisfies certain reality conditions---may be derived from an action principle involving a single scalar field and a single Lagrange multiplier with a non--derivative coupling to gravity.
26 pages, plain TEX