  Within the background-field framework we present a path integral derivation
of the splitting Ward identity for the one-particle irreducible effective
action in the presence of an infrared regulator, and make connection with
earlier works on the subject. The approach is general in the sense that it does
not rely on how the splitting is performed. This identity is then used to
address the problem of background dependence of the effective action at an
arbitrary energy scale. We next introduce the modified master equation and
emphasize its role in constraining the effective action. Finally, application
to general gauge theories within the geometric approach is discussed.
