**Contemporary Mathematics**

Volume: 434;
2007;
255 pp;
Softcover

MSC: Primary 53; 55; 58; 81;

Print ISBN: 978-0-8218-4062-7

Product Code: CONM/434

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

**Electronic ISBN: 978-0-8218-8113-2
Product Code: CONM/434.E**

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

# Geometric and Topological Methods for Quantum Field Theory

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*S. Paycha; B. Uribe*

This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures):

- Anomalies and noncommutative geometry,
- Deformation quantisation and Poisson algebras,
- Topological quantum field theory and orbifolds.

These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

#### Readership

Graduate students and research mathematicians interested in topological and geometric method in quantum field theory.

# Table of Contents

## Geometric and Topological Methods for Quantum Field Theory

- Contents v6 free
- Introduction vii8 free
- List of participants ix10 free
- Invited Lecturers 114 free
- Deformation Quantization: a Mini-Lecture 316
- Examples of noncommutative instantons 3952
- 1. Introduction 3952
- 2. Toric noncommutative manifolds 4053
- 3. Gauge theory on the sphere s4θ 4457
- 4. SU(2)-instantons on S4θ 5063
- 5. An instanton bundle over a symplectic quantum sphere S4q 5871
- Appendix A. Connections on noncommutative vector bundles 6780
- Appendix B. The Chern character of projections 7083
- References 7184

- Topological Quantum Field Theories, Strings and Orbifolds 7386
- Non-formal deformation quantization of Fréchet-Poisson algebras: The Heisenberg Lie algebra case 99112
- Anomalies and Noncommutative Index Theory 125138

- Contributed talks 161174
- N-flat connections 163176
- Dirac Equation in a Black Hole Background 173186
- Homological matrices 181194
- On Some Qualitative Properties of Stratified Flows 193206
- Property (T) and tensor products by irreducible finite dimensional representations for SLn(R) n ≥ 3 205218
- Painlevé VI equation from invariant instantons 215228
- Quantum Statistical Mechanics and Class Field Theory 223236
- Uniqueness of Kashiwara's quantization of complex contact manifolds 233246
- K-theoretic Gap labeling for Quasicrystals 247260