The Universal Renormalization Factors Z_1/Z_3 and Color Confinement Condition in Non-Abelian Gauge Theory

Abstract

The ratio Z_1/Z_3 of vertex and wave-function renormalization factors, which is universal (i.e., matter-independent), is shown to equal 1+u which gives the residue of the scalar pole $\propto p_μp_ν/p^2$ of 2-point function < D_μc D_ν\bar c >. This relation is interesting since 1+u=0 has been known to give a sufficient condition for color confinement. We also give an argument that, when 1+u=0 holds, it will be realized by the disappearance of the massless gauge boson pole and is related with the restoration of a certain ``local gauge symmetry&#34; as was discussed by Hata. (Talk given at International Symposium on BRS Symmetry, Sept.~18 -- 22, 1995, Kyoto.)