A Gauge Field Model On $SU(2)_L\times SU(2)_R\times U(1)_Y \times π_4(G_{YM})$

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We construct a gauge field model based on $SU(2)_L\times SU(2)_R\times U(1)_Y \times π_4(SU(2)_L\times SU(2)_R\times U(1)_Y) $ from the principle that both the original gauge group $G_{YM}$ and the discrete group $π_4(G_{YM})$ should be taken as gauge groups in the sense of non-commutative geometry. We show that the Yukawa coupling and the Higgs mechanism appear as natural results.
9 pages, LATEX

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