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

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Chapter 1. Introduction\n1.1 Quantum physics and classical electromagnetism\n1.2 Abelian Chern-Simons action\n1.3 Non-Abelian Chern-Simons action\nChapter 2. Basic notions of knot theory\n2.1 Ambient and regular isotopy\n2.2 Link invariants\n2.3 Framing and satellites\nChapter 3. Framing in field theory\n3.1 Abelian Chern-Simons theory\n3.2 Framed Wilson line operators\nChapter 4. Non-Abelian Chern-Simons theory\n4.1 Covariant quantization\n4.2 One-loop effective action\n4.3 Higher order results\nChapter 5. Observables and perturbation theory\n5.1 Wilson line operators\n5.2 Perturbative computations\nChapter 6. Properties of the expectation values\n6.1 Holonomy matrix\n6.2 Discrete symmetries\n6.3 Satellite formulae\nChapter 7. Ordering fermions and knot observables\n7.1 Ordering fermions\n7.2 Antiperiodic boundary conditions\n7.3 Knot observables\nChapter 8. Braid group\n8.1 Artin braid group\n8.2 Hecke algebra\nChapter 9. R-matrix and braids\n9.1 Quantum group approach\n9.2 Lie algebras and monodromy representations\n9.3 Quasi-Hopf algebra\nChapter 10. Chern-Simons monodromies\n10.1 Schrödinger picture\n10.2 Universality of the link invariants\n10.3 The inexistent shift\nChapter 11. Defining relations\n11.1 Calculus rules\nChapter 12. The extended Jones polynomial\n12.1 The values of the unknots\n12.2 Hopf link\n12.3 Trefoil knot\n12.4 Figure-eight knot\n12.5 Connection with the Jones polynomial\n12.6 Bracket connection\n12.7 Reconstruction theorems\nChapter 13. General properties\n13.1 Twist variable\n13.2 Recovered field theory\n13.3 Links in a solid torus\n13.4 Satellites\n13.5 Skein relation\n13.6 Projectors\n13.7 Borromean rings\n13.8 Connected sums\n13.9 Mutations\nChapter 14. Unitary groups\n14.1 Fundamental skein relation\n14.2 Casimir operator\n14.3 Composite states\n14.4 Pattern links\n14.5 Higher dimensional representations\n14.6 Polynomial structure\n14.7 SU(3) examples\nChapter 15. Reduced tensor algebra\n15.1 The restated solution\n15.2 Outlook\n15.3 Representation ring\n15.4 The three-sphere\n15.5 Reduced tensor algebra\n15.6 Roots of unity\n15.7 Special cases\nChapter 16. Surgery on three-manifolds\n16.1 Mapping class group of the torus\n16.2 Solid tori\n16.3 Dehn surgery\n16.4 Links in three-manifolds\n16.5 Elementary surgeries\n16.6 Physical interpretation\n16.7 The fundamental group\nChapter 17. Surgery and field theory\n17.1 Basic pairing\n17.2 Properties of the Hopf matrix\n17.3 Elementary surgery operators\n17.4 Surgery operator\n17.5 Surgery rules and Kirby moves\nChapter 18. Observables in three-manifolds\n18.1 The manifold S2 × S1\n18.2 The manifold RP3\n18.3 Lens spaces\n18.4 The Poincaré manifold\n18.5 The manifold T2 § S1\nChapter 19. Three-manifold invariant\n19.1 Improved partition function\n19.2 Values of the invariant\nChapter 20. Abelian surgery invariant\n20.1 Compact Abelian theory\n20.2 Abelian surgery rules\n20.3 Abelian surgery invariant\nReferences\nSubject Index