On a ZERO CURVATURE REPRESENTATION for BOSONIC STRINGS and P -BRANES

It is shown that a zero curvature representation for D– dimensional p–brane equations of motion originates naturally in the geometric (Lund– Regge– Omnes) approach. To study the possibility to use this zero curvature representation for investigation of nonlinear equations of p– branes, the simplest case of D– dimensional string (p = 1) is considered. The connection is found between the SO(1, 1) gauge (world–sheet Lorentz) invariance of the string theory with a nontrivial dependence on a spectral parameter of the Lax matrices associated with the nonlinear equations describing the embedding of a string world sheet into flat D– dimensional space – time. Namely, the spectral parameter can be identified with a parameter of constant SO(1, 1) gauge transformations, after the deformation of the Lax matrices has been performed.