2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53952In terms of non-commutative geometry, we show that the $σ$--model can be built up by the gauge theory on discrete group $Z_2$. We introduce a constraint in the gauge theory, which lead to the constraint imposed on linear $σ$ model to get nonlinear $σ$ model .High Energy Physics - Theorytext