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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...
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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...
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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...
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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...
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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...
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Some Noncommutative Spheres
Noncommutative geometry provides us various means to deal with noncommutative phenomena in mathematics, and C*-algebras (and von Neumann algebras)...
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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...
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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...
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Physical Properties
In Chap. 5 we studied solutions describing stationary counter-rotating dust disks in terms of hyperelliptic functions. As an example of this approach...
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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...
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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....
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Index
Abstract not available
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A. Proof of Thm. 4.34
Abstract not available
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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...
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Forces from Connes’ Geometry
Einstein derived general relativity from Riemannian geometry. Connes extends this derivation to noncommutative geometry and obtains electro–magnetic,...
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Lectures on Two-Dimensional Noncommutative Gauge Theory Quantization
These notes are devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with...
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Topological Quantum Field Theories and Operator Algebras
We have seen much fruitful interactions between 3-dimensional topology and operator algebras since the stunning discovery of the Jones polynomial for...
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Boundary Value Problems and Solutions
In the previous chapters we have used the complete integrability of the stationary axisymmetric Einstein equations in vacuum to construct and to...