Ludwik Dabrowski, Thomas Krajewski, Giovanni Landi
Some Properties of Non-linear $\sigma$-Models in Noncommutative Geometry
(51K, LaTex 2e)

ABSTRACT.  We introduce non-linear $\sigma$-models in the framework of 
noncommutative geometry with special emphasis on models defined on the 
noncommutative torus. We choose as target spaces the two point space and 
the circle and illustrate some characteristic features of the 
corresponding $\sigma$-models. 
In particular we construct a $\sigma$-model instanton with topological 
charge equal to $1$. We also define and investigate some properties of a 
noncommutative analogue of the Wess-Zumino-Witten model.