Question

Definition of gravity path integral?

Answer 1

A semiclassical no-boundary wave function is defined by an ensemble regular saddle points. The ensemble is restricted by simple considerations of symmetry such as time neutrality. ThePath Integral for Gravity. Cosmology, Quantum Gravity

Answer 2

Answer:

In a non-abelian gauge theory there is a "fundamental" gauge field Aaμ with gauge index a often called connection. Although Aaμ is not gauge invariant, gauge invariant quantities can be obtained from it. In particular the partition function in the path integral formulation is obtained schematically as:

Z[J]=∫[dAμ]eiS[A,∂A]+i∫J⋅A

Moreover, the associated field strength is given by

[Dμ,Dν]ψ=−iFμνψ

On the other hand, for gravity the usual logic is that from the "fundamental" metric tensor gμν