Perturbative reduction of derivative order in EFT
  Higher derivative corrections are ubiquitous in effective field theories,
which seemingly introduces new degrees of freedom at successive order. This is
actually an artefact of the implicit local derivative expansion defining
effective field theories. We argue that higher derivative corrections that
introduce additional degrees of freedom should be removed and their effects
captured either by lower derivative corrections, or special combinations of
higher derivative corrections not propagating extra derees of freedom. Three
methods adapted for this task are examined and field redefinitions are found to
be most appropriate. First order higher derivative corrections in a scalar
tensor theory are removed by field redefinition and it is found that their
effects are captured by a subset of Horndeski theories. A case is made for
restricting the effective field theory expansions in principle to only terms
not introducing additional degrees of freedom.
