The Principal chiral model as an integrable system

Referencias bibliográficas

• E. Beggs, Solitons in the chiral equation, Commun. Math. Phys. 128 (1990), 131–139.
• M. Bordemann, M. Forger, J. Laartz and U. Schäper, 2-dimensional nonlinear sigma models: zero curvature and Poisson structure, this volume.
• F.E. Burstall and J.H. Rawnsley, Twistor Theory for Riemannian Symmetric Spaces, Lect. Notes in Math. 1424, Springer, Berlin, 1990.
• I.V. Cherednik, Local conservations laws of principal chiral fields, Teo. Mat. Fiz. 38 (1979), 179–185; English transl.: Theor. Math. Phys. 38 (1979), 120.
• I. Cherednik, Algebraic aspects of two-dimensional chiral fields, Itogi Nauchn. i Tekhn Inform., Moscow, Ser. Sov. Prob. Mat. 17 (1981), 175–218, 220; English transl.: J. Soy. Math. 21 (1983), 601.
• I. Cherednik, Definition of functions for generalized affine Lie algebras, Funk. Anal. Prilozh. 17 (1983), 93–95; English transl.: Func. Anal. Appl. 17 (1983), 243–245.
• I. Cherednik, Elliptic curves and soliton matrix differential equations, Itogi Nauchn. i Tekhn. Inform., Moscow, Alg. Top. Geom. 22 (1984), 205–265, 267; English transi.: J.Sov.Math. 38 (1987), 1989.
• L. Dickey, Symplectic structure, Lagrangian and involutiveness of first integrals of the principal chiral model, Commun. Math. Phys. 87 (1983), 505–513.
• B.A. Dubrovin, A.T. Fomenko and S.P. Novikov, Modern Geometry - Methods and Applications: The Geometry and Topology of Manifolds, Springer, Berlin, 1985.
• B.A. Dubrovin, I.Krichever and S.P. Novikov, Integrable Systems I, in: Encyclopaedia of Mathematical Science 4 (Dynamical Systems IV), V.I. Arnold and S.P. Novikov (eds.), Springer, Berlin, 1990.
• L. Faddeev and L. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Springer, Berlin, 1987.
• M.A. Guest and Y.Ohnita, Group actions and deformations of harmonic maps,J. Math. Soc. Japan. (to appear).
• F.Guil and M. Manas, The Homogeneous Heisenberg subalgebra and equations of AKNS type, Lett. Math.Phys. 19 (1990), 89–95.
• F. Guil and M. Manas, Two-dimensional integrable systems and self-dual Yang-Mills equations,Preprint FT/UCM/18/92.
• N. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math.Soc. 55 (1987), 59–126.
• D.A. Korotkin, Finite-gap solutions of the SU(1,1) and SU(2) duality equations and their axisymmetric steady-state reductions, Mat. Sbornik 181 (1990), 923–933; English transi.: Math. USSR Sbornik 70 (1991), 355.
• D.A. Korotkin, Self-dual Yang-Mills fields and deformations of algebraic curves, Commun. Math.Phys. 134 (1990), 397–412.
• S.P. Novikov, S. Manakov, L. Piatveskii and V.E. Zakharov, Theory of Solitons (The Inverse Scattering Method), Consultants Bureau, New York, 1984.
• A. Ogielski, M. Prasad, A. Sinha and L. Chau, Biicklund transformations and local conservation laws for principal chiral fields, Phys. Lett. 91B (1980), 387–391.
• B. Piette and W.J. Zakrzewski, General solutions of the U(3) and U141 chiral a Models in two dimensions, Nucl. Phys. B300 (1988), 207–222.
• K. Pohlmeyer, Integrable Hamiltonian systems and interactions through quadratic constraints, Commun. Math.Phys. 46 (1976), 207–221.
• A. Pressley and G.Segal, Loop groups, Oxford University Press, Oxford, 1986.
• -118,221; English transl.: J. Sov. Math. 46 (1989), 1631.
• G. Segal, Loop Groups and Harmonic Maps, in: Advances in Homotopy Theory, London Math Soc.Lect. Notes 139, B. Salamon, B. Steer and W. Sutherland (eds.), Cambridge University Press, Cambridge, 1989, 153.
• M. Semenov-Tyan-Shanskii, Classical r-Matrices, Lax Equations, Poisson-Lie Groups and Dressing Transformations, in: Field Theory, Quantum Gravity and Strings II, Lect. Notes Phys. 280, H.de Vega and N. Sànchez (eds.), Springer, Berlin, 1987, 174.
• K. Uhlenbeck, Harmonic maps into Lie groups (Classical solutions of the chiral model), J. Diff. Geom. 30 (1989), 1–50.
• K. Uhlenbeck, On the connection between harmonic maps and the self-dual Yang-Mills and the sine-Gordon Equation, J. Geom. Phys. 8 (1992), 283–316.
• R. Ward, Classical solutions of the chiral model, unitons, and holomorphic vector bundles, Commun. Math. Phys. 128 (1990), 319–332.
• J.C. Wood, Explicit construction and parametrization of harmonic two-spheres in the unitary group, Proc. London Math. Soc. 58 (1989), 608–624.
• J.C. Wood, Harmonic maps into symmetric spaces and integrable systems,this volume.
• V.E. Zakharov and A.V. Mikhailov, Relativistically invariant two—dimensional model of field theory which is integrable by means of the inverse scattering problem method, Zh. Eksp. Teor.Fiz. 74 (1978), 1953–1973; English transi Sov. Phys. JETP 47 (1978) 1017–1027.
• V.E. Zakharov and A.V. Mikhailov, On the integrability of classical spinor models in two-dimensional space-time, Commun. Math. Phys. 74 (1980), 21–40.
• V.E. Zakharov and A.V. Shabat Integration of nonlinear equations of Mathematical—Physics by inverse scattering II, Funk Anal. Prilozh. 13 (1978), 13–22; English transl • Func. Anal. Appl. 13 (1979), 166–174.