for a different number of gravitons at different positions. Or, one could use the two-field formalism, treating as an independent field so that the wave function is . Mathematical formalism The Wheeler–DeWitt equation is a functional differential equation. It is ill-defined in the general case, but very important in theoretical physics, especially in quantum gravity. It is a functional differential equation on the space of three dimensional spatial metrics. The Wheeler–DeWitt equation has the form of an operator acting on a wave functional; the functional reduces to a function in cosmology. Contrary to the general case, the Wheeler–DeWitt equation is well defined in minisuperspaces like the configuration space of cosmological theories. An example of such a wave function is the Hartle–Hawking state. Bryce DeWitt first published this equation in 1967 under the name "Einstein–Schrödinger equation"; it was later renamed the "Wheeler–DeWitt equation". Hamiltonian constraint Simply speaking, the Wheeler–DeWitt equation says where is the Hamiltonian constraint in quantized general relativity and stands for the wave function of the universe. Unlike ordinary quantum field theory or quantum mechanics, the Hamiltonian is a first class constraint on physical states. We also have an independent constraint for each point in space. Although the symbols and may appear familiar, their interpretation in the Wheeler–DeWitt equation is substantially different from non-relativistic quantum mechanics. is no longer a spatial wave function in the traditional sense of a complex-valued function that is defined on a 3-dimensional space-like surface and normalized to unity. Instead it is a functional of field configurations on all of spacetime. This wave function contains all of the information about the geometry and matter content of the universe. is still an operator that acts on the Hilbert space of wave functions, but it is not the same Hilbert space as in the nonrelativistic case, and the Hamiltonian no longer determines evolution of the system, so the Schrödinger equation no longer applies. This property is known as timelessness. The reemergence of time requires the tools of decoherence and clock operators (or the use of a scalar field). Momentum constraint We also need to augment the Hamiltonian constraint with momentum constraints associated with spatial diffeomorphism invariance. In minisuperspace approximations, we only have one Hamiltonian constraint (instead of infinitely many of them). In fact, the principle of general covariance in general relativity implies that global evolution per se does not exist; the time is just a label we