Ground State Functional of the Linearized Gravitational Field

The ground state functional of the linearized Einstein theory of gravitation is given as a functional of the gauge invariant Ricci tensor, and compared with the corresponding electromagnetic expression. The connection of the canonically quantized nonlinear theory of gravitation with the linearized theory is exhibited. Time is treated as a momentum variable rather than as a superspace coordinate, which leads to an ``extrinsic time representation'' hTTik, hi, t = −½Δ−1πT. The state functional of the linearized theory is shown to be the initial value of the state functional of the canonical theory on a constant extrinsic time hypersurface in the lowest order of a perturbation expansion. By means of the Einstein-Schrödinger equation, this functional can be integrated off this initial hypersurface.