Introduction to Quantum Group and Integrable Massive Models of Quantum Field Theory

The Proceedings consists of 6 lectures each from Prof L Takhtajan and Prof F Smirnov which were presented during the workshop.

• Lectures on Integrable Massive Models of Quantum Field Theory (F A Smirnov):
  • General Problems of the Quantum Field Theory. Completely Integrable Models
  • Space of States. Form Factors. A Set of Axioms for Form Factors
  • Local Commutativity and Asymptotic Conditions
  • Form Factors in SU(2)-Invariant Thirring Model
  • Necessary Properties of the Currents Form Factors in SU(2)-Invariant Thirring Model
  • Properties of Currents in SU(2)-Invariant Thirring Model
• Lectures on Quantum Groups (L A Takhtajan):
  • Historical Introduction. Algebraic Background
  • Poisson-Lie Groups, CYBE and Modified CYBE. Connection with ISM. Lie-Algebraic Meaning of CYBE and Modified CYBE
  • Quantization Procedure as a Deformation of the Algebra of Classical Observables
  • Weyl Quantization. Quantization of Poisson-Lie Groups Associated with CYBE
  • QYBE
  • Quantization of Poisson-Lie Groups Associated with Modified CYBE. Quantum Matrix Algebras. Quantum Determinant and Quantum Groups SL(n) and GL (n)
  • Quantum Vector Spaces for the Quantum Groups SL_q(n), GL_q(n) and their Real Forms. Quantum Groups O_q(N), SP_q(n), Quantum Vector Spaces Associated with them and their Real Forms
  • Quantization of the Universal Enveloping Algebras of the Simple Lie Algebras. Elements of the Representations Theory