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  1. Topological Concepts in Gauge Theories

    In these lecture notes, an introduction to topological concepts and methods in studies of gauge field theories is presented. The three paradigms of...
    F. Lenz in Topology and Geometry in Physics
    Chapter

  2. Chiral Anomalies and Topology

    When a field theory has a symmetry, global or local like in gauge theories, in the tree or classical approximation formal manipulations lead to...
    J. Zinn-Justin in Topology and Geometry in Physics
    Chapter

  3. A. Proof of Thm. 4.34

    Abstract not available
    Frédéric Cao in Geometric Curve Evolution and Image Processing
    Chapter

  4. Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method

    We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e....
    Micheline Musette in Direct and Inverse Methods in Nonlinear Evolution Equations
    Chapter

  5. Sato Theory and Transformation Groups. A Unified Approach to Integrable Systems

    More than 20 years ago, it was discovered that the solutions of the Kadomtsev-Petviashvili (KP) hierarchy constitute an infinite-dimensional...
    Ralph Willox, Junkichi Satsuma in Discrete Integrable Systems
    Chapter

  6. Discrete Painlevé Equations: A Review

    We present a review of what is current knowledge about discrete Painlevé equations. We start with a historical introduction which explains how the...
    B. Grammaticos, A. Ramani in Discrete Integrable Systems
    Chapter

  7. Index

    Abstract not available
    Frédéric Cao in Geometric Curve Evolution and Image Processing
    Chapter

  10. Ultradiscrete Systems (Cellular Automata)

    Ultradiscretization is a limiting procedure which allows one to obtain a cellular automaton (CA) from continuous equations. Using this method, we can...
    Tetsuji Tokihiro in Discrete Integrable Systems
    Chapter

  11. Symmetries of Discrete Systems

    In this series of lectures, we review the application of Lie point symmetries, and their generalizations, to the study of difference equations. The...
    Pavel Winternitz in Discrete Integrable Systems
    Chapter

  12. Time in Science: Reversibility vs. Irreversibility

    To discuss properly the question of irreversibility one needs to make a careful distinction between reversibility of the equations of motion and the...
    Yves Pomeau in Discrete Integrable Systems
    Chapter

  13. Secondary Characteristic Classes of Lie Algebroids

    We show how the intrinsic characteristic classes of Lie algebroids can be seen as characteristic classes of representations. We present two...
    M. Crainic, R.L. Fernandes in Quantum Field Theory and Noncommutative Geometry
    Chapter

  14. Some Noncommutative Spheres

    Noncommutative geometry provides us various means to deal with noncommutative phenomena in mathematics, and C*-algebras (and von Neumann algebras)...
    T. Natsume in Quantum Field Theory and Noncommutative Geometry
    Chapter

  15. Local Models for Manifolds with Symplectic Connections of Ricci Type*

    We show that any symplectic manifold (Mω) of dimension 2n(n≥ 2) admitting a symplectic connection of Ricci type can locally be constructed by a...
    M. Cahen in Quantum Field Theory and Noncommutative Geometry
    Chapter

  16. Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces

    I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on...
    R. Wulkenhaar in Geometric and Topological Methods for Quantum Field Theory
    Chapter

  17. An Infinite Family of Isospectral Pairs Topological Aspects

    We give some basic properties of the isospectral pairs (Γ,Γ) of two bipartite graphs Γ and Γ. Then we present a systematic method of constructing an...
    N. Iiyori, T. Itoh, ... T. Masuda in Quantum Field Theory and Noncommutative Geometry
    Chapter

  18. Noncommutative Line Bundles and Gerbes

    We introduce noncommutative line bundles and gerbes within the framework of deformation quantization. The Seiberg-Witten map is used to construct the...
    B. Jurčo in Quantum Field Theory and Noncommutative Geometry
    Chapter

  19. From Quantum Tori to Quantum Homogeneous Spaces

    We construct dual objects for quantum complex projective spaces as quantum homogeneous spaces of quantum unitary groups, in which the deformation...
    S. Kamimura in Quantum Field Theory and Noncommutative Geometry
    Chapter

  20. Index Theorems and Noncommutative Topology

    These lecture notes are mainly devoted to a K-theory proof of the Atiyah-Singer index theorem. Some applications of the K-theory to noncommutative...
    T. Fack in Geometric and Topological Methods for Quantum Field Theory
    Chapter
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