Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-10-30
Phys.Lett.B388:35-44,1996
Physics
High Energy Physics
High Energy Physics - Theory
14 pages. LATEX. Revised version. Submitted to Phys. Lett. B. The arrangement of the material is changed. Some additional refe
Scientific paper
10.1016/0370-2693(96)01162-8
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.
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