Euclidean quantum gravity

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.

References

G. W. Gibbons and S. W. Hawking (eds.), Euclidean quantum gravity , World Scientific (1993)