Relation To ADM Formalism
Euclidean Quantum Gravity does relate back to ADM formalism used in canonical quantum gravity and recovers the Wheeler–DeWitt equation under various circumstances. If we have some matter field, then the path integral reads
where integration over includes an integration over the three-metric, the lapse function, and shift vector . But we demand that be independent of the lapse function and shift vector at the boundaries, so we obtain
where is the three-dimensional boundary. Observe that this expression vanishes implies the functional derivative vanishes, giving us the Wheeler-DeWitt equation. A similar statement may be made for the Diffeomorphism constraint (take functional derivative with respect to the shift functions instead).
Read more about this topic: Euclidean Quantum Gravity
Famous quotes containing the words relation to, relation and/or formalism:
“We must get back into relation, vivid and nourishing relation to the cosmos and the universe. The way is through daily ritual, and is an affair of the individual and the household, a ritual of dawn and noon and sunset, the ritual of the kindling fire and pouring water, the ritual of the first breath, and the last.”
—D.H. (David Herbert)
“The foregoing generations beheld God and nature face to face; we, through their eyes. Why should not we also enjoy an original relation to the universe? Why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us, and not the history of theirs?”
—Ralph Waldo Emerson (1803–1882)
“It is sentimentalism to assume that the teaching of life can always be fitted to the child’s interests, just as it is empty formalism to force the child to parrot the formulas of adult society. Interests can be created and stimulated.”
—Jerome S. Bruner (20th century)