UID:
almahu_9947360001102882
Format:
Online-Ressource (xiv, 312 p)
,
ill
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
3110140284
,
9783110140286
,
9783110879643
Series Statement:
De Gruyter expositions in mathematics 10
Note:
Includes bibliographical references (p. [303]-309) and index
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10.3 The inexistent shiftChapter 11. Defining relations; 11.1 Calculus rules; Chapter 12. The extended Jones polynomial; 12.1 The values of the unknots; 12.2 Hopf link; 12.3 Trefoil knot; 12.4 Figure-eight knot; 12.5 Connection with the Jones polynomial; 12.6 Bracket connection; 12.7 Reconstruction theorems; Chapter 13. General properties; 13.1 Twist variable; 13.2 Recovered field theory; 13.3 Links in a solid torus; 13.4 Satellites; 13.5 Skein relation; 13.6 Projectors; 13.7 Borromean rings; 13.8 Connected sums; 13.9 Mutations; Chapter 14. Unitary groups; 14.1 Fundamental skein relation.
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14.2 Casimir operator14.3 Composite states; 14.4 Pattern links; 14.5 Higher dimensional representations; 14.6 Polynomial structure; 14.7 SU(3) examples; Chapter 15. Reduced tensor algebra; 15.1 The restated solution; 15.2 Outlook; 15.3 Representation ring; 15.4 The three-sphere; 15.5 Reduced tensor algebra; 15.6 Roots of unity; 15.7 Special cases; Chapter 16. Surgery on three-manifolds; 16.1 Mapping class group of the torus; 16.2 Solid tori; 16.3 Dehn surgery; 16.4 Links in three-manifolds; 16.5 Elementary surgeries; 16.6 Physical interpretation; 16.7 The fundamental group.
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5.2 Perturbative computationsChapter 6. Properties of the expectation values; 6.1 Holonomy matrix; 6.2 Discrete symmetries; 6.3 Satellite formulae; Chapter 7. Ordering fermions and knot observables; 7.1 Ordering fermions; 7.2 Antiperiodic boundary conditions; 7.3 Knot observables; Chapter 8. Braid group; 8.1 Artin braid group; 8.2 Hecke algebra; Chapter 9. R-matrix and braids; 9.1 Quantum group approach; 9.2 Lie algebras and monodromy representations; 9.3 Quasi-Hopf algebra; Chapter 10. Chern-Simons monodromies; 10.1 Schrödinger picture; 10.2 Universality of the link invariants.
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Chapter 1. Introduction; 1.1 Quantum physics and classical electromagnetism; 1.2 Abelian Chern-Simons action; 1.3 Non-Abelian Chern-Simons action; Chapter 2. Basic notions of knot theory; 2.1 Ambient and regular isotopy; 2.2 Link invariants; 2.3 Framing and satellites; Chapter 3. Framing in field theory; 3.1 Abelian Chern-Simons theory; 3.2 Framed Wilson line operators; Chapter 4. Non-Abelian Chern-Simons theory; 4.1 Covariant quantization; 4.2 One-loop effective action; 4.3 Higher order results; Chapter 5. Observables and perturbation theory; 5.1 Wilson line operators.
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Chapter 17. Surgery and field theory17.1 Basic pairing; 17.2 Properties of the Hopf matrix; 17.3 Elementary surgery operators; 17.4 Surgery operator; 17.5 Surgery rules and Kirby moves; Chapter 18. Observables in three-manifolds; 18.1 The manifold S2 × S1; 18.2 The manifold RP3; 18.3 Lens spaces; 18.4 The Poincaré manifold; 18.5 The manifold T2 S1; Chapter 19. Three-manifold invariant; 19.1 Improved partition function; 19.2 Values of the invariant; Chapter 20. Abelian surgery invariant; 20.1 Compact Abelian theory; 20.2 Abelian surgery rules; 20.3 Abelian surgery invariant; References.
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Subject Index.
Language:
English
DOI:
10.1515/9783110879643
URL:
http://www.degruyter.com/doi/book/10.1515/9783110879643