  We study the operator product expansion of two non-interacting chiral
currents in the presence of external gauge fields in four dimensional euclidean
space. We obtain the operator singularity in terms of the beta function of the
free energy density and a connection on the space of external gauge fields, by
imposing the consistency between the variational formula, introduced previously
by the author, and both the renormalization group equations and the equation of
motion for the currents. As a byproduct, we derive a euclidean version of the
anomalous commutator of two currents in an appendix.
