The Wheeler–DeWitt equation is a field equation. It is part of a theory that attempts to combine mathematically the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity. In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called 'problem of time'. More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergman–Komar "group" (which is the diffeomorphism...

The Hamiltonian constraint arises from any theory that admits a Hamiltonian formulation and is reparametrisation-invariant. The Hamiltonian constraint of general relativity is an important non-trivial example. In the context of general relativity, the Hamiltonian constraint technically refers to a linear combination of spatial and time diffeomorphism constraints reflecting the reparametrizability of the theory under both spatial as well as time coordinates. However, most of the time the term Hamiltonian constraint is reserved for the constraint that generates time diffeomorphisms. == Simplest... ==

In general relativity, the Gibbons–Hawking–York boundary term is a term that needs to be added to the Einstein–Hilbert action when the underlying spacetime manifold has a boundary. The Einstein–Hilbert action is the basis for the most elementary variational principle from which the field equations of general relativity can be defined. However, the use of the Einstein–Hilbert action is appropriate only when the underlying spacetime manifold M {\displaystyle {\mathcal {M}}} is closed, i.e., a manifold which is...