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New Symmetry Principles in Quantum Field Theory

  • Book
  • © 1992

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Editors:
  1. J. Fröhlich

    1. ETH-Zürich, Zürich, Switzerland

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  2. G. Hooft

    1. Institute for Theoretical Physics, Utrecht, The Netherlands

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  3. A. Jaffe

    1. Harvard University, Cambridge, USA

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  4. G. Mack

    1. II Institut für Theoretische Physik, Hamburg, Germany

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  5. P. K. Mitter

    1. University of Paris VI, Paris, France

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  6. R. Stora

    1. Laboratory of Particle Physics, Annecy, Annecy-le-Vieux, France

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Part of the book series: NATO Science Series B: (NSSB, volume 295)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-viii
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  2. Lecturers

    1. Quantum Symmetries in 2D Massive Field Theories

      • Denis Bernard
      Pages 1-35

    2. On Knot and Manifold Invariants

      • Raoul Bott
      Pages 37-52

    3. The Metric Aspect of Noncommutative Geometry

      • Alain Connes, John Lott
      Pages 53-93

    4. Intersection Theory, Integrable Hierarchies and Topological Field Theory

      • Robbert Dijkgraaf
      Pages 95-158

    5. Quantum Symmetry in Conformal Field Theory by Hamiltonian Methods

      • L. D. Faddeev
      Pages 159-175

    6. Observables, Superselection Sectors and Gauge Groups

      • Claus Fredenhagen
      Pages 177-194

    7. Incompressible Quantum Fluids, Gauge-Invariance, and Current Algebra

      • Jürg Fröhlich, Urban M. Studer
      Pages 195-246

    8. Non-compact WZW Conformal Field Theories

      • Krzysztof Gawȩdzki
      Pages 247-274

    9. S-Matrix Theory for Black Holes

      • G. ’t Hooft
      Pages 275-294

    10. Non-Commutative Geometry and Mathematical Physics

      • Arthur Jaffe
      Pages 295-308

    11. Whitham Theory for Integrable Systems and Topological Quantum Field Theories

      • I. Krichever
      Pages 309-327

    12. Quantum Symmetry in Quantum Theory

      • Gerhard Mack, Volker Schomerus
      Pages 329-353

    13. Quantum Groups in Lattice Models

      • V. Pasquier
      Pages 355-380

    14. Lagrangian Conformal Models

      • Raymond Stora
      Pages 381-381

    15. Semi-classical Liouville Theory, Complex Geometry of Moduli Spaces, and Uniformization of Riemann Surfaces

      • Leon Takhtajan
      Pages 383-406
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Keywords

About this book

Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad­ vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al­ gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par­ ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte­ grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.

Editors and Affiliations

  • ETH-Zürich, Zürich, Switzerland

    J. Fröhlich

  • Institute for Theoretical Physics, Utrecht, The Netherlands

    G. Hooft

  • Harvard University, Cambridge, USA

    A. Jaffe

  • II Institut für Theoretische Physik, Hamburg, Germany

    G. Mack

  • University of Paris VI, Paris, France

    P. K. Mitter

  • Laboratory of Particle Physics, Annecy, Annecy-le-Vieux, France

    R. Stora

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