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A new gauge fixing that imposes the U(1) real and quaternion real conditionon the correlator of domain wall fermion on the left wall and right wall isproposed. The method is applied to the calculation of the mass function, theQCD effective coupling and the charge form factor of the proton. By assumingtopological charge change $|Q|=1$, the charge form factor of the proton isapproximately fitted by the dipole form factor.  The difference of the Kugo-Ojima color confinement parameter in quenchedsimulation and in unquenched simulation is expected to be due to an anomalycaused by the vertex of two fermion zero modes and the Bose ghost/gluon.

Self-dual gauge fields, domain wall fermion zero modes and the Kugo-Ojima confinement criterion