Quantum Field Theory and Noncommutative Geometry

G. Landi (auth.), Ursula Carow-Watamura, Yoshiaki Maeda, Satoshi Watamura (eds.)9783540239000, 3-540-23900-6, 3540239006

This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on “Quantum Field Theory and Noncommutative Geometry.” A considerable effort has been invested in making the contributions accessible to a wider community of readers – so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.

Table of contents :
Noncommutative Spheres and Instantons….Pages 1-56
Some Noncommutative Spheres….Pages 57-66
From Quantum Tori to Quantum Homogeneous Spaces….Pages 67-74
Local Models for Manifolds with Symplectic Connections of Ricci Type * ….Pages 75-87
On Gauge Transformations of Poisson Structures….Pages 89-112
Classification of All Quadratic Star Products on a Plane * ** ….Pages 113-126
Universal Deformation Formulae for Three-Dimensional Solvable Lie Groups….Pages 127-141
Morita Equivalence, Picard Groupoids and Noncommutative Field Theories….Pages 143-155
Secondary Characteristic Classes of Lie Algebroids….Pages 157-176
Gauge Theories on Noncommutative Spacetime Treated by the Seiberg-Witten Method * ….Pages 177-192
Noncommutative Line Bundles and Gerbes….Pages 193-204
Lectures on Two-Dimensional Noncommutative Gauge Theory Quantization….Pages 205-237
Topological Quantum Field Theories and Operator Algebras….Pages 239-253
Topological Quantum Field Theory and Algebraic Structures * ….Pages 255-287
An Infinite Family of Isospectral Pairs Topological Aspects….Pages 289-297