The quantization of gravity: The quantization of the full Einstein equations

We quantized the full Einstein equations in a globally hyperbolic spacetime $N=N^{n+1}$, $n\ge 3$, and found solutions of the resulting hyperbolic equation in a fiber bundle $E$ which can be expressed as a product of spatial eigenfunctions (eigendistributions) and temporal eigenfunctions. The spatial eigenfunctions form a basis in an appropriate Hilbert space while the temporal eigenfunctions are solutions to a second order ordinary differential equation in ${\mathbb{R}}_{+}$. In case $n\ge 17$ and provided the cosmological constant $\mathrm{\Lambda }$ is negative the temporal eigenfunctions are eigenfunctions of a self-adjoint operator ${\widehat{H}}_0$ such that the eigenvalues are countable and the eigenfunctions form an orthonormal basis of a Hilbert space.