2.6 The measure
One can derive non-trivial conditions on the lattice measure by imposing the Slavnov–Taylor identities
in a perturbative lattice calculation. Starting from the general form of the measure for Poincaré gravity,
Menotti and Pelissetto  performed a one-loop calculation and found that the Slavnov–Taylor identity
can be satisfied for a particular choice of , (momentum expansion coefficients of ), and of
the cosmological constant . The solution still depends on a real parameter (related to a residual
non-invariance under rotations). This makes it difficult to draw any immediate conclusions on the structure
of the full, non-perturbative measure.