Euclidean quantum gravity refers to a Wick rotated version of quantum gravity, formulated as a quantum field theory. The manifolds that are used in this formulation are 4 dimensional Riemannian manifolds instead of pseudo Riemannian manifolds. It is also assumed that the manifolds are compact, connected and boundaryless (i.e. no singularities). Following the usual quantum field-theoretic formulation, the vacuum to vacuum amplitude is written as a functional integral over the metric tensor, which is now the quantum field under consideration.
where φ denotes all the matter fields. See Einstein-Hilbert action.
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Famous quotes containing the word quantum:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)