Geometrodynamics regained

The Bohm Interpretation of Quantum Cosmology

“…We now recall the result of Ref. [45]. There it is shown that a general super-hamiltonianH which satisfies Eq.…”

“…This is because many strong results concerning geometrodynamics were obtained in this later picture [45,58]. We will construct a hamiltonian formalism which is consistent with the guidance relations (27) and (28).…”

The Superspace of geometrodynamics

“…The proof of the theorem is given in [51], which improves on earlier versions [41,74] in that the latter assumes in addition that H[h, π] be an even function of π , corresponding to the requirement of time reversibility of the generated evolution. This was overcome in [51] by the clever move to write the condition set by {H (α 1 , 0), H (α 2 , 0)} = H (0, β ) (the right-hand side being already known) on H (α, 0) in terms of the corresponding Lagrangian functional L, which is then immediately seen to turn into a condition which is linear in L, so that terms with even powers in velocity decouple form those with odd powers.…”

From topological to parametrized field theory

“…(For a full explanation of this point as well as of all other properties of our constraint algebra, see Hojman et al [6].) We now have a diffeomorphism invariant theory that describes matter propagating on a flat background.…”

“…On the constraint surface φ a I = 0 this is the usual constraint algebra of general relativity. It is the fingerprint of diffeomorphism invariance in a metric space in the Hamiltonian formulation, having the geometrical interpretation [6] as the algebra of deformations of spatial hypersurfaces in a Lorentzian spacetime. From this point of view the matrix η IJ is an object that is inserted in the phase space action precisely in order to make a geometrical interpretation of the solutions possible.…”