  We propose that the low energy behavior of a pure gauge theory can be studied
by simply assuming violation of Lorentz invariance which is implemented through
a deformation of the canonical Poisson brackets of the theory depending on an
infrared scale. The resulting theory is equivalent to a pure gauge theory with
a Chern-Simons like term. It is shown that at low energies this theory can be
identified with three dimensional QCD where the mass of the fermion is related
to the infrared scale.
