Consistency of Hamiltonian diagonalization for field theories in a Robertson-Walker background

It is shown that by performing an appropriate time-dependent canonical transformation on the action for a scalar field theory in a Robertson-Walker background one can obtain a Hamiltonian whose ground state {}v;t₀〉 at any initial time t₀ has several desirable properties. First of all its field anticommutator expectation values G(x,y) =〈v;t₀{}{{φ}(x),{φ}(y)}{}v;t₀〉@BB are of the Hadamard form: G(x,y)→_x→y(1/4π²)[1/{σ} +1/2[M²+({ξ}-(1/6))R]ln ({σ})+O(σ⁰)], where {}2{σ} is the geodesic distance between x and y, for all values of t₀. Second, the divergent part of the energy density is independent of t₀, thus allowing a state-independent renormalization of the energy density. If the appropriate canonical transformation is not performed, the aforementioned results fail to hold.