Geometric and Topological Methods for Quantum Field Theory

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.

Spis treści:
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.