The Complete Solution of the Classical SL(2,R)/U(1) Gauged WZNW Field Theory

Abstract

We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand-Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto canonical free fields. The results will, finally, be collected in a local Bäcklund transformation. These calculations prepare the theory for an exact canonical quantization.

20 pages, no figures, LaTeX, uses amsfonts

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