Nonlinear two-dimensionalσ-model instanton as a tunneling process

We study the instanton in the nonlinear two-dimensional $\sigma$ model and show that it can be interpreted, in Minkowski space, as a tunneling process through a potential barrier between two vacuums. In this case the process carries nontrivial winding number. We then show, using this interpretation, that the $\sigma$-model vacuum is nevertheless unique by demonstrating that two such vacuums may also be connected by processes that carry zero winding number and which do not require tunneling through a barrier. Some geometrical aspects of instanton solutions are also given.