Possible interpretation on the origin of four-fermion interaction

We present a possible interpretation on the origin of the four-fermion interaction used in effective field theories. Inspired by the sharp momentum peak seen in Bose-Einstein condensate state, we incorporate the special gluon condensate effect into the gluon propagator. We then find that, if one considers hypothetic situation with the condensed gluon, the four-fermion contact interaction can arise from the first principle theory of quantum chromodynamics.