Communications in Mathematical Physics

, Volume 142, Issue 1, pp 99–138 | Cite as

Quantum group symmetries and non-local currents in 2D QFT

  • Denis Bernard
  • André LeClair


We construct and study the implications of some new non-local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions, including the sine-Gordon theory and its generalization to affine Toda theory. These non-local currents provide a non-perturbative formulation of the theories. The symmetry algebras correspond to the quantum affine Kac-Moody algebras. TheS-matrices are completely characterized by these symmetries. FormalS-matrices for the imaginary-coupling affine Toda theories are thereby derived. The application of theseS-matrices to perturbed coset conformal field theory is studied. Non-local charges generating the finite dimensional Quantum Group in the Liouville theory are briefly presented. The formalism based on non-local charges we describe provides an algernative to the quantum inverse scattering method for solving integrable quantum field theories in 2d.


Neural Network Nonlinear Dynamics Group Symmetry Quantum Computing Quantum Group 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Denis Bernard
    • 1
  • André LeClair
    • 2
  1. 1.Service de Physique Théorique de SaclayGif-sur-YvetteFrance
  2. 2.Newman Laboratory of Nuclear StudiesCornell UniversityIthacaUSA

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