Test of the Kugo-Ojima Confinement Criterion in the Lattice Landau Gauge

and (F ×G) = fabcF G. Under the assumption that BRS singlets have positive metric, it is proved that Vphys has positive semidefinite in such a way that BRS quartet particles appear only in zero norm. One finds from the BRS transformation that for each colour a, a set of massless asymptotic fields χ, β, γ, γ̄ form a BRS quartet. The Noether current corresponding to the conservation of the colour symmetry is gJ μ = ∂F a μν + {QB, Dμc̄}, where its ambiguity by divergence of antisymmetric tensor should be understood, and this ambiguity is utilised so that massless contribution may be eliminated for the charge, Q, to be well defined. Denoting g(Aμ × c̄) a → uab∂μγ̄ , and then Dμc̄ a → (1+u)ab∂μγ̄ , one obtains the eq.(*) provided Aμ has a vanishing expectation value. The current {QB, Dμc̄} contains the massless component, (1 + u)b∂μβ (x). We can modify the Noether current for colour charge Q such that