We analyze the integrability properties of models defined on the symmetric
space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach fo
r integrable theories in any dimension. We point out the key ingredients fo
r a theory to possess an infinite number of local conservation laws, and di
scuss classes of models with such property, We propose a 3 + 1-dimensional,
relativistic invariant field theory possessing a toroidal soliton solution
carrying a unit of topological charge given by the Hopf map. Construction
of the action is guided by the requirement that the energy of static config
uration should be scale invariant. The solution is constructed exactly. The
model possesses an infinite number of local conserved currents. The method
is also applied to the Skyrme-Faddeev model, and integrable submodels are
proposed. (C) 1999 Elsevier Science B.V. All rights reserved.