- Euclidean quantum gravity
**Euclidean quantum gravity**refers to a Wick rotated version ofquantum gravity , formulated as aquantum field theory . Themanifold s that are used in this formulation are 4 dimensionalRiemannian manifold s instead ofpseudo Riemannian manifold s. It is also assumed that the manifolds arecompact , connected and boundaryless (i.e. no singularities). Following the usual quantum field-theoretic formulation, thevacuum to vacuum amplitude is written as a functional integral over themetric tensor , which is now the quantum field under consideration.:$int\; mathcal\{D\}old\{g\},\; mathcal\{D\}phi,\; expleft(-int\; d^4x\; sqrt(R+mathcal\{L\}\_mathrm\{matter\})\; ight)$

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)

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