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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... -
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... -
A. Proof of Thm. 4.34
Abstract not available -
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.... -
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... -
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... -
Index
Abstract not available -
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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... -
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... -
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... -
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... -
Some Noncommutative Spheres
Noncommutative geometry provides us various means to deal with noncommutative phenomena in mathematics, and C*-algebras (and von Neumann algebras)... -
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... -
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... -
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... -
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... -
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... -
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...