Lecture notes on Chern-Simons-Witten theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Angekündigt als: Hu, Sen: Witten's lectures on three dimensional topological quantum field theory Includes bibliographical references and index |
| Physical Description: | XII, 200 S. graph. Darst. |
| ISBN: | 9810239084 9810239092 |
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| 100 | 1 | |a Hu, Sen |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lecture notes on Chern-Simons-Witten theory |c Sen Hu |
| 246 | 1 | 3 | |a m |
| 246 | 1 | 3 | |a Witten's lectures on three dimensional topological quantum field theory |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2001 | |
| 300 | |a XII, 200 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Angekündigt als: Hu, Sen: Witten's lectures on three dimensional topological quantum field theory | ||
| 500 | |a Includes bibliographical references and index | ||
| 600 | 1 | 4 | |a Witten, Edward |
| 650 | 4 | |a Champs de jauge (Physique) | |
| 650 | 4 | |a Champs, Théorie quantique des - Mathématique | |
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| 650 | 7 | |a Invarianten |2 gtt | |
| 650 | 4 | |a Invariants | |
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| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 4 | |a Quantification géométrique | |
| 650 | 4 | |a Variétés topologiques à 3 dimensions | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Gauge fields (Physics) | |
| 650 | 4 | |a Geometric quantization | |
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Quantum field theory |x Mathematics | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
Chapter 1 Examples of Quantizations 1
1.1 Quantization of R2 1
1.1.1 Classical mechanics 1
1.1.2 Symplectic method 3
1.1.3 Holomorphic method 6
1.2 Holomorphic representation of symplectic quotients and its quan¬
tization 7
1.2.1 An example of circle action 7
1.2.2 Moment map of symplectic actions 9
1.2.3 Some geometric invariant theory 11
1.2.4 Grassmanians 12
1.2.5 Calabi Yau/Ginzburg Landau correspondence 13
1.2.6 Quantization of symplectic quotients 14
Chapter 2 Classical Solutions of Gauge Field Theory 17
2.1 Moduli space of classical solutions of Chern Simons action ... 17
2.1.1 Symplectic reduction of gauge fields over a Riemann surface 17
2.1.2 Chern Simons action on a three manifold 19
2.2 Maxwell equations and Yang Mills equations 22
2.2.1 Maxwell equations 22
2.2.2 Yang Mills equations 23
2.3 Vector bundle, Chern classes and Chern Weil theory 25
2.3.1 Vector bundle and connection 25
be
x Contents
2.3.2 Curvature, Chern classes and Chern Weil theory .... 26
Chapter 3 Quantization of Chern Simons Action 27
3.1 Introduction 27
3.2 Some formal discussions on quantization 28
3.3 Pre quantization 31
3.3.1 M. as a complex variety 31
3.3.2 Quillen s determinant bundle on M. and the Laplacian . 32
3.4 Some Lie groups 32
3.4.1 G=R 32
3.4.2 G = S1 = R/2ttZ 33
3.4.3 T*G 34
3.5 Compact Lie groups, G = SU(2) 35
3.5.1 Genus one 35
3.5.2 Riemann sphere with punctures 36
3.5.3 Higher genus Riemann surface 38
3.5.4 Relation with WZW model and conformal field theory . 39
3.6 Independence of complex structures 40
3.7 Borel Weil Bott theorem of representation of Lie groups .... 44
Chapter 4 Chern Simons Witten Theory and Three Mani¬
fold Invariant 47
4.1 Representation of mapping class group and three manifold in¬
variant 47
4.1.1 Knizhik Zamolodchikov equations and conformal blocks 48
4.1.2 Braiding and fusing matrices 50
4.1.3 Projective representation of mapping class group .... 53
4.1.4 Three dimensional manifold invariants via Heegard de¬
composition 57
4.2 Calculations by topological quantum field theory 59
4.2.1 Atiyah s axioms 59
4.2.2 An example: connected sum 60
4.2.3 Jones polynomials 60
4.2.4 Surgery 61
4.2.5 Verlinde s conjecture and its proof 63
4.3 A brief survey on quantum group method 64
4.3.1 Algebraic representation of knot 64
4.3.2 Hopf algebra and quantum groups 67
Contents xi
4.3.3 Chern Simons theory and quantum groups 68
Chapter 5 Renormalized Perturbation Series of Chern Simons
Witten Theory 71
5.1 Path integral and morphism of Hilbert spaces 71
5.1.1 One dimensional quantum field theory 71
5.1.2 Schroedinger operator 72
5.1.3 Spectrum and determinant 75
5.2 Asymptotic expansion and Feynman diagrams 77
5.2.1 Asymptotic expansion of integrals, finite dimensional case 77
5.2.2 Integration on a sub variety 81
5.3 Partition function and topological invariants 82
5.3.1 Gauge fixing and Faddeev Popov ghosts 83
5.3.2 The leading term 85
5.3.3 Wilson line and link invariants 88
5.4 A brief introduction on renormalization of Chern Simons theory 89
5.4.1 A regulization scheme 90
5.4.2 The Feynman rules 91
Chapter 6 Topological Sigma Model and Localization 95
6.1 Constructing knot invariants from open string theory 95
6.1.1 Introduction 95
6.1.2 A topological sigma model 96
6.1.3 Localization principle 97
6.1.4 Large TV expansion of Chern Simons gauge theory ... 98
6.2 Equivariant cohomology and localization 99
6.2.1 Equivariant cohomology 99
6.2.2 Localization, finite dimensional case 100
6.3 Atiyah Bott s residue formula and Duistermaat Heckman formulalOl
6.3.1 Complex case, Atiyah Bott s residue formula 101
6.3.2 Symplectic case, Duistermaat Heckman formula .... 102
6.4 2D Yang Mills theory by localization principle 104
6.4.1 Cohomological Yang Mills field theory 104
6.4.2 Relation with physical Yang Mills theory 105
6.4.3 Evaluation of Yang Mills theory 107
6.5 Combinatorial approach to 2D Yang Mills theory 110
xii Contents
Complex Manifold Without Potential Theory by S. S. Chern 113
Geometric Quantization of Chern Simons Gauge Theory
by S. Axelrod, S. D. Pietra and E. Witten 121
On Holomorphic Factorization of WZW and Coset Models 169
Bibliography 193
Index 197
Afterwards 199
|
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| language | English |
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| spelling | Hu, Sen Verfasser aut Lecture notes on Chern-Simons-Witten theory Sen Hu m Witten's lectures on three dimensional topological quantum field theory Singapore [u.a.] World Scientific 2001 XII, 200 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Angekündigt als: Hu, Sen: Witten's lectures on three dimensional topological quantum field theory Includes bibliographical references and index Witten, Edward Champs de jauge (Physique) Champs, Théorie quantique des - Mathématique IJkinvariantie gtt Invarianten gtt Invariants Kwantumveldentheorie gtt Manifolds gtt Quantification géométrique Variétés topologiques à 3 dimensions Mathematik Gauge fields (Physics) Geometric quantization Quantum field theory Mathematics Three-manifolds (Topology) Chern-Simons-Feldtheorie (DE-588)4335725-8 gnd rswk-swf Chern-Simons-Feldtheorie (DE-588)4335725-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009516442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hu, Sen Lecture notes on Chern-Simons-Witten theory Witten, Edward Champs de jauge (Physique) Champs, Théorie quantique des - Mathématique IJkinvariantie gtt Invarianten gtt Invariants Kwantumveldentheorie gtt Manifolds gtt Quantification géométrique Variétés topologiques à 3 dimensions Mathematik Gauge fields (Physics) Geometric quantization Quantum field theory Mathematics Three-manifolds (Topology) Chern-Simons-Feldtheorie (DE-588)4335725-8 gnd |
| subject_GND | (DE-588)4335725-8 |
| title | Lecture notes on Chern-Simons-Witten theory |
| title_alt | m Witten's lectures on three dimensional topological quantum field theory |
| title_auth | Lecture notes on Chern-Simons-Witten theory |
| title_exact_search | Lecture notes on Chern-Simons-Witten theory |
| title_full | Lecture notes on Chern-Simons-Witten theory Sen Hu |
| title_fullStr | Lecture notes on Chern-Simons-Witten theory Sen Hu |
| title_full_unstemmed | Lecture notes on Chern-Simons-Witten theory Sen Hu |
| title_short | Lecture notes on Chern-Simons-Witten theory |
| title_sort | lecture notes on chern simons witten theory |
| topic | Witten, Edward Champs de jauge (Physique) Champs, Théorie quantique des - Mathématique IJkinvariantie gtt Invarianten gtt Invariants Kwantumveldentheorie gtt Manifolds gtt Quantification géométrique Variétés topologiques à 3 dimensions Mathematik Gauge fields (Physics) Geometric quantization Quantum field theory Mathematics Three-manifolds (Topology) Chern-Simons-Feldtheorie (DE-588)4335725-8 gnd |
| topic_facet | Witten, Edward Champs de jauge (Physique) Champs, Théorie quantique des - Mathématique IJkinvariantie Invarianten Invariants Kwantumveldentheorie Manifolds Quantification géométrique Variétés topologiques à 3 dimensions Mathematik Gauge fields (Physics) Geometric quantization Quantum field theory Mathematics Three-manifolds (Topology) Chern-Simons-Feldtheorie |
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