A Gauge Field Model On $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_Y\times {\pi }_4(G_{YM})$

Abstract

We construct a gauge field model based on $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_Y\times {\pi }_4(SU(2{)}_L\times SU(2{)}_R\times U(1{)}_Y)$ from the principle that both the original gauge group $G_{YM}$ and the discrete group ${\pi }_4(G_{YM})$ 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.

Comments: 9 pages, LATEX