The Link Invariants of the Chern-Simons Field Theory : New Developments in Topological Quantum Field Theory

Description

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2018) Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021) Content: Frontmatter -- Chapter 1. Introduction -- Chapter 2. Basic notions of knot theory -- Chapter 3. Framing in field theory -- Chapter 4. Non-Abelian Chern-Simons theory -- Chapter 5. Observables and perturbation theory -- Chapter 6. Properties of the expectation values -- Chapter 7. Ordering fermions and knot observables -- Chapter 8. Braid group -- Chapter 9. R-matrix and braids -- Chapter 10. Chern-Simons monodromies -- Chapter 11. Defining relations -- Chapter 12. The extended Jones polynomial -- Chapter 13. General properties -- Chapter 14. Unitary groups -- Chapter 15. Reduced tensor algebra -- Chapter 16. Surgery on three-manifolds -- Chapter 17. Surgery and field theory -- Chapter 18. Observables in three-manifolds -- Chapter 19. Three-manifold invariant -- Chapter 20. Abelian surgery invariant -- References -- Subject Index -- Backmatter.