  We provide the reformulations of Yang-Mills theories in terms of gauge
invariant metric-like variables in three and four dimensions. The
reformulations are used to analyze the dimension two gluon condensate and give
gauge invariant descriptions of gluon polarization. In three dimensions, we
obtain a non-zero dimension two gluon condensate by one loop computation, whose
value is similar to the square of photon mass in the Schwinger model. In four
dimensions, we obtain a Lagrangian with the dual property, which shares the
similar but different property with the dual superconductor scenario. We also
make discussions on the effectiveness of one loop approximation.
