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.God does not care about our mathematical difficulties. He integrates empirically.Albert Einstein

FZZ Scattering

“…As in Liouville theory, this mapping to free fields is canonical [29,30,31]. Expanding the fields φ, φ in modes as…”

“…The classical equations of the cigar non-linear sigma model were solved in terms of free fields in [29,30,31]. This solution was canonically quantized in the interesting work [32].…”

“…In this section we will address a similar scattering problem formulated in the cigar background (1.1). The classical equations of the cigar non-linear sigma model were solved in terms of free fields in [29,30,31]. This solution was canonically quantized in the interesting work [32].…”

“…The exact solution to this equation found in [29,30,31] in terms of two free fields φ(z, z) = φ(z)+ φ(z) and X(z, z) = X(z) + X(z) reads…”