On the physical interpretation of the Vilkovisky-Dewitt effective action

This letter examines the physical interpretation of a class of reparameterization-invariant effective actions, recently introduced by DeWitt. These include as a special case the Vilkovisky and DeWitt effective action. The invariant actions are shown to share those features at the root of the utility of the standard effective action. In particular, they can be interpreted as the minimum energy in states that are subject to a reparameterization-invariant constraint. It is also shown that, contrary to standard lore, although the Vilkovisky-DeWitt action is given as the sum of one-particle-irreducible graphs it is not the generator of 1PI n-point functions