The complete solution of the classical \(\text{SL}(2,\mathbb{R})/\text{U}(1)\) gauged WZNW field theory. (English) Zbl 0937.37056
The presence of the Lax pair representation for any gauged WZNW model is established. An explicit general solution of the classical equations of motion of the \(SL(2,\mathbb{R})/ U(1)\) theory is given. Its symplectic structure is calculated by solving an initial state problem of a Gelfand-Dikii type equation. On this basis the authors derive a nonlocal canonical free-field transformation of the nonlinear fields of the theory and collect these transformations in a local Bäcklund transformation. The calculations are done for a field-theoretic situation with asymptotic boundary conditions.
Reviewer: Samir Musayev (Baku)
MSC:
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
