  The effective action formalism introduced by Vilkovisky and later modified by
DeWitt is completely covariant suitable for obtaining an effective action that
is independent of the parametrization of the quantum fields. Among a few basic
properties of an effective action, one property is that it can be written as a
sum of one-particle irreducible diagrams. In this work, we verify this property
up to three-loop order for Vilkovisky-Dewitt effective action (VDEA) by solving
the equations satisfied by VDEA written down in the original parametrization
for non-gauge theories.
