  The derivation of effective equations for group field theories is discussed
from a variational point of view, with the action being determined by the
fidelity of the trial state with respect to the exact state. It is shown how
the maximisation procedure with respect to the parameters of the trial state
lead to the expected equations, in the case of simple condensates. Furthermore,
we show that the second functional derivative of the fidelity gives a compact
way to estimate, within the effective theory itself, the limits of its
validity. The generalisation can be extended to include the Nakajima--Zwanzig
projection method for general mixed trial states.
