Abstract
Nucl.Phys.B529:689-736,1998 The zero curvature representation for two dimensional integrable models is
generalized to spacetimes of dimension d+1 by the introduction of a d-form
connection. The new generalized zero curvature conditions can be used to
represent the equations of motion of some relativistic invariant field theories
of physical interest in 2+1 dimensions (BF theories, Chern-Simons, 2+1 gravity
and the CP^1 model) and 3+1 dimensions (self-dual Yang-Mills theory and the
Bogomolny equations). Our approach leads to new methods of constructing
conserved currents and solutions. In a submodel of the 2+1 dimensional CP^1
model, we explicitly construct an infinite number of previously unknown
nontrivial conserved currents. For each positive integer spin representation of
sl(2) we construct 2j+1 conserved currents leading to 2j+1 Lorentz scalar
charges.
