# Geometric and Topological Methods for Quantum Field Theory

Cambridge University Press

Edition: Illustrated, 4/29/2010

EAN 9780521764827, ISBN10: 0521764823

Hardcover, 434 pages, 25.4 x 18 x 2.5 cm

Language: English

Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.

Introduction

1. The impact of QFT on low-dimensional topology Paul Kirk

2. Differential equations aspects of quantum cohomology Martin A. Guest

3. Index theory and groupoids Claire Debord and Jean-Marie Lescure

4. Renormalization Hopf algebras and combinatorial groups Alessandra Frabetti

5. BRS invariance for massive boson fields JosÃƒÂ© M. Gracia-BondÃƒÂa

6. Large N field theories and geometry David Berenstein

7. Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity Martin Reuter and Frank Saueressig

8. When is a differentiable manifold the boundary of an orbifold? AndrÃƒÂ©s Angel

9. Canonical group quantization, rotation generators and quantum indistinguishability Carlos Benavides and AndrÃƒÂ©s Reyes-Lega

10. Conserved currents in KÃƒÂ¤hler manifolds Jaime R. Camacaro and Juan Carlos Moreno

11. A symmetrized canonical determinant on odd-class pseudodifferential operators Marie-FranÃƒÂ§oise Ouedraogo

12. Some remarks about cosymplectic metrics on maximal flag manifolds Marlio Paredes and Sofia PinzÃƒÂ³n

13. Heisenberg modules over real multiplication noncommutative tori and related algebraic structures Jorge Plazas

Index.