Consequences of path-integral discretizations that render the magnetic Weyl term a normalization factor

Determine the physical consequences and consistency of path-integral discretizations in which the magnetic part of the Weyl curvature contributes only to the normalization in the classical-quantum gravity path integral, and clarify their implications for handling negative-definite directions and extending the framework to dynamical spacetimes.

Background

The diffusion action employs a generalized DeWitt metric that is not positive semidefinite; certain negative contributions are argued to be non-dynamical (e.g., Gauss–Bonnet, magnetic Weyl). The authors note that specific discretizations can make the magnetic Weyl term contribute only to normalization, apparently rendering it benign.

However, they caution that the consequences of this treatment are not fully understood, especially for dynamical spacetimes and boundary terms, and that care is needed before extending the approach beyond the static scenarios analyzed in the paper.