Problems of modern quantum field theory : invited lectures of the Spring School, held in Alushta USSR, April 24-May 5, 1989
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書誌事項
Problems of modern quantum field theory : invited lectures of the Spring School, held in Alushta USSR, April 24-May 5, 1989
（Research reports in physics）
Springer-Verlag, c1989
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Includes bibliographical references and index
内容説明・目次
内容説明
This volume is the compilation of invited lectures presented at the Spring School "Problems of Modern Quantum Field Theory" held in Alushta (USSR) April 24-May 5 1989, organized by the Institute for Theoretical Physics (Kiev) and Landau Institute for Theoretical Physics (Moscow). Approximately one hundred physicists and mathematicians attended lectures on aspects of mod- ern quantum field theory: Conformal Field Theory, Geometrical Quantization, Quantum Groups and Knizhnik-Zamolodchikov Equations, Non-Archimedian Strings, Calculations on Riemannian Surfaces. A number of experts active in research in these areas were present and they shared their ideas in both formal lectures and informal conversations. V. Drinfeld discusses the relation between quasi-Hopf algebras, conformal field theory, and knot invariants. The author sketches a new proof of Konno's theorem on the equivalence of the braid group representations corresponding to R-matrices and the Knizhnik-Zamolodchikov equation. The main ideas of quantum analogs of simple Lie superalgebras and their dual objects - algebras of functions on the quantum supergroup - are introduced in the paper by P.P. Kulish.
He proposes the universal R-matrix for simplest superalgebra osp(2/1) and discusses the elements of a representation theory. In the paper by A. Alekseev and S. Shatashvili the correspondence between geometrical quantization and conformal field theory is established. It allows one to develop a Lagrange approach to two-dimensional conformal field theory. The authors also discuss the relation to finite R-matrices.
目次
Quasi-Hopf Algebras and Knizhnik-Zamolodchikov Equations.- Quantum Lie Superalgebras and Supergroups.- From Geometric Quantization to Conformal Field Theory.- Bosonization of Wess-Zumino-Witten Models and Related Conformal Theories.- The Cutting and Sewing Method in String Theory.- P-Adic String World Sheets: Higher Genera.- Virasoro Action on Riemann Surfaces, Grassmannians, det $${\bar \partial _J}$$ and Segal-Wilson ?-Function.- On the Superextension of the Kadomtsev-Petviashvili Equation and Finite-Gap Solutions of Korteweg-de Vries Superequations.- Finite Size Effects in Conformal Field Theories and Non-local Operators in One-Dimensional Quantum Systems.- The Solution of the Two-Dimensional Ising Model with Magnetic Fields Applied to the Boundaries.- On the Relativistic Field Theories with Fractional Statistics and Spin in D=(2+1), (3+1).- Electron on a Surface in an External Magnetic Field: Hidden Supersymmetry, Zero Modes and Boundary Conditions.- Index of Contributors.
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