  Starting with conformally covariant correlation functions, a sequence of
functional representations of the conformal algebra is constructed. A key step
is the introduction of representations which involve an auxiliary functional.
It is observed that these functionals are not arbitrary but rather must satisfy
a pair of consistency equations corresponding to dilatation and special
conformal invariance. In a particular representation, the former corresponds to
the canonical form of the Exact Renormalization Group equation specialized to a
fixed-point whereas the latter is new. This provides a concrete understanding
of how conformal invariance is realized as a property of the Wilsonian
effective action and the relationship to action-free formulations of conformal
field theory.
  Subsequently, it is argued that the conformal Ward Identities serve to define
a particular representation of the energy-momentum tensor. Consistency of this
construction implies Polchinski's conditions for improving the energy-momentum
tensor of a conformal field theory such that it is traceless. In the Wilsonian
approach, the exactly marginal, redundant field which generates lines of
physically equivalent fixed-points is identified as the trace of the
energy-momentum tensor.
