Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics 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 wishing to thoroughly study the topic.
Editorial Board
Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Chapter
3.2 Framed Wilson line operators
pp.：
37 – 39
3.1 Abelian Chern-Simons theory
pp.：
37 – 37
Chapter 4. Non-Abelian Chern-Simons theory
pp.：
39 – 45
4.2 One-loop effective action
pp.：
45 – 48
4.1 Covariant quantization
pp.：
45 – 45
4.3 Higher order results
pp.：
48 – 53
Chapter 5. Observables and perturbation theory
pp.：
53 – 56
5.2 Perturbative computations
pp.：
56 – 58
5.1 Wilson line operators
pp.：
56 – 56
Chapter 6. Properties of the expectation values
pp.：
58 – 61
6.1 Holonomy matrix
pp.：
61 – 61
6.2 Discrete symmetries
pp.：
61 – 63
6.3 Satellite formulae
pp.：
63 – 64
Chapter 7. Ordering fermions and knot observables
pp.：
64 – 72
7.1 Ordering fermions
pp.：
72 – 72
7.2 Antiperiodic boundary conditions
pp.：
72 – 74
7.3 Knot observables
pp.：
74 – 78
Chapter 8. Braid group
pp.：
78 – 80
8.1 Artin braid group
pp.：
80 – 80
8.2 Hecke algebra
pp.：
80 – 83
Chapter 9. R-matrix and braids
pp.：
83 – 88
9.1 Quantum group approach
pp.：
88 – 88
9.2 Lie algebras and monodromy representations
pp.：
88 – 93
9.3 Quasi-Hopf algebra
pp.：
93 – 94
Chapter 10. Chern-Simons monodromies
pp.：
94 – 97
10.1 Schrödinger picture
pp.：
97 – 97
10.2 Universality of the link invariants
pp.：
97 – 101
10.3 The inexistent shift
pp.：
101 – 104
Chapter 11. Defining relations
pp.：
104 – 106
Chapter 12. The extended Jones polynomial
pp.：
106 – 116
11.1 Calculus rules
pp.：
106 – 106
12.2 Hopf link
pp.：
116 – 122
12.1 The values of the unknots
pp.：
116 – 116
12.3 Trefoil knot
pp.：
122 – 124
12.4 Figure-eight knot
pp.：
124 – 126
12.5 Connection with the Jones polynomial
pp.：
126 – 132
12.6 Bracket connection
pp.：
132 – 134
12.7 Reconstruction theorems
pp.：
134 – 136
Chapter 13. General properties
pp.：
136 – 141
13.2 Recovered field theory
pp.：
141 – 144
13.1 Twist variable
pp.：
141 – 141
13.3 Links in a solid torus
pp.：
144 – 147
13.4 Satellites
pp.：
147 – 152
13.5 Skein relation
pp.：
152 – 155
13.6 Projectors
pp.：
155 – 159
13.7 Borromean rings
pp.：
159 – 161
13.8 Connected sums
pp.：
161 – 167
13.9 Mutations
pp.：
167 – 170
Chapter 14. Unitary groups
pp.：
170 – 175
14.1 Fundamental skein relation
pp.：
175 – 175
14.2 Casimir operator
pp.：
175 – 178
14.3 Composite states
pp.：
178 – 182
14.4 Pattern links
pp.：
182 – 186
14.5 Higher dimensional representations
pp.：
186 – 190
14.6 Polynomial structure
pp.：
190 – 193
14.7 SU(3) examples
pp.：
193 – 195
Chapter 15. Reduced tensor algebra
pp.：
195 – 201
15.1 The restated solution
pp.：
201 – 201
15.2 Outlook
pp.：
201 – 204
15.3 Representation ring
pp.：
204 – 206
15.4 The three-sphere
pp.：
206 – 209
15.5 Reduced tensor algebra
pp.：
209 – 210
15.6 Roots of unity
pp.：
210 – 215
15.7 Special cases
pp.：
215 – 218
Chapter 16. Surgery on three-manifolds
pp.：
218 – 222
16.2 Solid tori
pp.：
222 – 223
16.1 Mapping class group of the torus
pp.：
222 – 222
16.3 Dehn surgery
pp.：
223 – 228
16.4 Links in three-manifolds
pp.：
228 – 231
16.5 Elementary surgeries
pp.：
231 – 234
16.6 Physical interpretation
pp.：
234 – 236
16.7 The fundamental group
pp.：
236 – 238
Chapter 17. Surgery and field theory
pp.：
238 – 242
17.1 Basic pairing
pp.：
242 – 242
17.2 Properties of the Hopf matrix
pp.：
242 – 245
17.3 Elementary surgery operators
pp.：
245 – 251
17.4 Surgery operator
pp.：
251 – 257
17.5 Surgery rules and Kirby moves
pp.：
257 – 260
Chapter 18. Observables in three-manifolds
pp.：
260 – 263
18.2 The manifold RP3
pp.：
263 – 272
18.1 The manifold S2 × S1
pp.：
263 – 263
18.3 Lens spaces
pp.：
272 – 276
18.4 The Poincaré manifold
pp.：
276 – 280
18.5 The manifold T2 § S1
pp.：
280 – 283
Chapter 19. Three-manifold invariant
pp.：
283 – 286
19.2 Values of the invariant
pp.：
286 – 292
19.1 Improved partition function
pp.：
286 – 286
Chapter 20. Abelian surgery invariant
pp.：
292 – 297
20.2 Abelian surgery rules
pp.：
297 – 303
20.1 Compact Abelian theory
pp.：
297 – 297
20.3 Abelian surgery invariant
pp.：
303 – 306
References
pp.：
306 – 317
Subject Index
pp.：
317 – 325
The Link Invariants of the Chern-Simons Field Theory
：New Developments in Topological Quantum Field Theory
( De Gruyter Expositions in Mathematics )
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