  In the context of scalar quantum field theory we introduce a class of
generically nonlinear quantum-background splits for which the splitting Ward
identity, encoding the single field dependence in the effective action, can be
solved exactly. We show that this can be used to construct an effective action
which is both covariant and dependent on the background and fluctuation fields
only through a single total field in a way independent from the dynamics.
Moreover we discuss the criteria under which the ultraviolet symmetries are
inherited by the quantum effective action. The approach is demonstrated through
some examples, including the $O(N)$ effective field theory, which might be of
interest for the Higgs sector of the Standard Model or its extensions.
