ABSTRACT
It is presented an approach to construct a zero curvature representation for integrable theories in spacetimes of dimension d + 1 by the introduction of a d-form connection. It generalizes in a quite natural way the well known Lax and Zakharov-Shabat equations for two dimensional integrable models. We show that some sufficient conditions to make the zero curvature equation local involve, in an interesting way, non-semisimple Lie algebras and their representations. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest. Our approach leads to new methods of constructing conserved currents and solutions. We discuss in detail the example of the 2 + 1 dimensional CP 1 model. For one of its submodels we explicitly construct an infinite number of nontrivial local conserved currents.
