Overview

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.

Full Product Details

Author:   Hernan Ocampo (Universidad del Valle, Colombia) ,  Eddy Pariguan (Pontificia Universidad Javeriana, Colombia) ,  Sylvie Paycha (Université de Clermont-Ferrand II (Université Blaise Pascal), France)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
ISBN:  

9780511712135

ISBN 10:   0511712138
Publication Date:   07 September 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   In stock  
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Table of Contents

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 José M. Gracia-Bondía; 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? Andrés Angel; 9. Canonical group quantization, rotation generators and quantum indistinguishability Carlos Benavides and Andrés Reyes-Lega; 10. Conserved currents in Kähler manifolds Jaime R. Camacaro and Juan Carlos Moreno; 11. A symmetrized canonical determinant on odd-class pseudodifferential operators Marie-Françoise Ouedraogo; 12. Some remarks about cosymplectic metrics on maximal flag manifolds Marlio Paredes and Sofia Pinzón; 13. Heisenberg modules over real multiplication noncommutative tori and related algebraic structures Jorge Plazas; Index.

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Author Information

Hernán Ocampo is a Professor of Theoretical Physics at the University del Valle, Colombia. Eddy Pariguán is an Associate Professor in Mathematics at the University La Javeriana, Colombia. Sylvie Paycha is a Professor of Mathematics at the University Blaise Pascal, France.

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