  The structure of the gaussian auxiliary field approximation in the theory of
phase ordering kinetics is analysed with the aim of placing the method within
the context of a systematic theory. While we are unable to do this for systems
with a scalar order parameter, where the approximation remains uncontrolled, a
systematic development about the gaussian approximation can be outlined for
systems with a vector order parameter in terms of a suitably defined
$1/N$-expansion.
