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

Abstract

We reconstruct the Lagrangian of a left-right symmetric model with the gauge group $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_Y\times {\pi }_4(SU(2{)}_L\times SU(2{)}_R\times U(1{)}_Y)$. The Higgs fields appear as gauge fields on discrete gauge group ${\pi }_4(SU(2{)}_L\times SU(2{)}_R\times U(1{)}_Y)$ and are assigned in a way complying with 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 sense of non-commutative geometry.

9 pages, LaTex, AS-ITP-94-35