Chaotic field theory: a sketch

Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characteriz ing the chaotic dynamics, as well as the starting semiclassical approximati on to the quantum theory. New methods for computing corrections to the semi classical approximation are developed; in particular, a nonlinear field tra nsformation yields the perturbative corrections in a form more compact than the Feynman diagram expansions. (C) 2000 Elsevier Science B.V. All rights reserved.