Hamiltonian reduction of spin-two theory and of solvable cosmologies

TL;DR

This paper applies Hamiltonian reduction to spin-two fields and solvable cosmologies, revealing gauge invariance issues and implications for quantum gravity, especially in the context of Robertson-Walker models.

Contribution

It demonstrates Hamiltonian reduction for spin-two fields using the Faddeev-Jackiw method and explores its implications for General Relativity and quantum cosmology.

Findings

Reduced Hamiltonian contains only traceless-transverse fields

Not all non-propagating components are determined by constraints

Operator ordering in Wheeler-DeWitt equation is fixed by reduced dynamics

Abstract

The Hamiltonian reduction of the massless spin-two field theory is carried out following the Faddeev-Jackiw approach. The reduced Hamiltonian contains only the traceless-transverse fields, but not all of the non-propagating components can be determined by the constraints of the theory. The reason for this is found in the fact that the Hamiltonian is not gauge invariant. Consequences and implications for General Relativity are discussed and illustrated on the example of Robertson-Walker cosmologies with a scalar field. Also, it it shown that for those explicitely solvable models, the reduced form of the dynamics uniquely determines the operator ordering that has to be adopted in the Wheeler-DeWitt equation in order to maintain consistency.