Quantization, classical and quantum field theory, and theta functions:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2003
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| Series: | CRM monograph series
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 136 p. ill. : 26 cm |
| ISBN: | 0821832409 |
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MARC
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| 100 | 1 | |a Tjurin, Andrej N. |d 1940-2002 |e Verfasser |0 (DE-588)114078807 |4 aut | |
| 245 | 1 | 0 | |a Quantization, classical and quantum field theory, and theta functions |c Andrei Tyurin |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2003 | |
| 300 | |a xii, 136 p. |b ill. : 26 cm | ||
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Record in the Search Index
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| adam_text | Contents
Foreword vii
Editor s note viii
Introduction ix
Chapter 1. Quantization Procedure 1
1.1. The framework 1
1.2. Real polarization (Symplectic Geometry) 3
1.3. Kahler quantization (Algebraic Geometry) 5
1.4. Extended Kodaira Spencer theory 7
1.5. Faithful functors 13
1.6. Perfect quantization 14
Chapter 2. Algebraic Curves = Riemann Surfaces 17
2.1. Direct approach 17
2.2. Jacobians 17
2.3. Algebro geometrical theory of theta functions 18
2.4. Symplectic combinatorial theory of theta functions 19
2.5. Abelian holomorphic flat connections 24
2.6. Perfect quantization 27
Chapter 3. Non Abelian Theta Functions 29
3.1. Algebraic geometry of moduli spaces of vector bundles 29
3.2. Holomorphic flat connections 31
3.3. Moduli of stable pairs and the desingularization of moduli spaces 35
3.4. Holomorphic symplectic geometry of Higgs fields 36
3.5. Gauge theory on Riemann surface. Higgs fields 38
3.6. Complex polarization of CLRep(7ri(E),SU(2)) 42
3.7. Computations of ranks 44
3.8. Hitchin s connections 48
Chapter 4. Symplectic Geometry of Moduli Spaces of Vector Bundles 53
4.1. Goldman U(l) action 53
4.2. Real polarization 55
4.3. Bohr Sommerfeld fibers 57
4.4. Delzant model 61
Chapter 5. Two Versions of CQFT 63
5.1. WZW version 63
5.2. WZW connection 67
5.3. Monodromy representations 67
xi
xii CONTENTS
Chapter 6. Three Valent Graphs 71
6.1. Spin networks 71
6.2. Three dimensional topology 72
6.3. Geometry of graphs 74
6.4. Circle complex and graph complex 81
6.5. Gauge theory on graphs 87
6.6. Abelian gauge theory and U(l) spin networks 89
6.7. Harmonic analysis of SU(2) spin networks 92
6.8. RCFT and Kohno representation 94
Chapter 7. Analytical Aspects of the Theory of Non Abelian Theta
Functions 101
7.1. The unitary Schottky space 101
7.2. ^ extended Hall s construction of CST for SU(2) 101
Chapter 8. BPU Map 107
8.1. Geometry of Lagrangian cycles 107
8.2. Legendre distributions 109
8.3. Geodesic lifting 113
Chapter 9. The Main Weapon 117
9.1. Large limit curves 117
9.2. Canonical classes and canonical maps 118
9.3. Special 1 parameter deformation of large limit curves 120
9.4. Special 2 parameter deformations of large limit curves 123
9.5. Modular configuration 126
9.6. Pico( Pr) and moduli spaces M*l(Pr) of 11 curves 127
9.7. Compactifications and AG theory of theta functions for 11 curves 130
Bibliography 133
|
| any_adam_object | 1 |
| author | Tjurin, Andrej N. 1940-2002 |
| author_GND | (DE-588)114078807 |
| author_facet | Tjurin, Andrej N. 1940-2002 |
| author_role | aut |
| author_sort | Tjurin, Andrej N. 1940-2002 |
| author_variant | a n t an ant |
| building | Verbundindex |
| bvnumber | BV020828933 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.G46 |
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| callnumber-sort | QC 3174.17 G46 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 240 SK 370 UO 4000 |
| ctrlnum | (OCoLC)52858190 (DE-599)BVBBV020828933 |
| dewey-full | 530.14/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/3 |
| dewey-search | 530.14/3 |
| dewey-sort | 3530.14 13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV020828933 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:20:11Z |
| institution | BVB |
| isbn | 0821832409 |
| language | English |
| lccn | 2003061207 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013834178 |
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| owner | DE-703 DE-384 DE-83 DE-11 |
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| physical | xii, 136 p. ill. : 26 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | CRM monograph series |
| series2 | CRM monograph series |
| spelling | Tjurin, Andrej N. 1940-2002 Verfasser (DE-588)114078807 aut Quantization, classical and quantum field theory, and theta functions Andrei Tyurin Providence, RI American Mathematical Society 2003 xii, 136 p. ill. : 26 cm txt rdacontent n rdamedia nc rdacarrier CRM monograph series 21 Kwantumveldentheorie gtt Theta-functies gtt Functions, Theta Geometric quantization Quantum field theory Thetafunktion (DE-588)4185175-4 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Thetafunktion (DE-588)4185175-4 s Geometrische Quantisierung (DE-588)4156720-1 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 CRM monograph series 21 (DE-604)BV007928388 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013834178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tjurin, Andrej N. 1940-2002 Quantization, classical and quantum field theory, and theta functions CRM monograph series Kwantumveldentheorie gtt Theta-functies gtt Functions, Theta Geometric quantization Quantum field theory Thetafunktion (DE-588)4185175-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd |
| subject_GND | (DE-588)4185175-4 (DE-588)4047984-5 (DE-588)4156720-1 |
| title | Quantization, classical and quantum field theory, and theta functions |
| title_auth | Quantization, classical and quantum field theory, and theta functions |
| title_exact_search | Quantization, classical and quantum field theory, and theta functions |
| title_full | Quantization, classical and quantum field theory, and theta functions Andrei Tyurin |
| title_fullStr | Quantization, classical and quantum field theory, and theta functions Andrei Tyurin |
| title_full_unstemmed | Quantization, classical and quantum field theory, and theta functions Andrei Tyurin |
| title_short | Quantization, classical and quantum field theory, and theta functions |
| title_sort | quantization classical and quantum field theory and theta functions |
| topic | Kwantumveldentheorie gtt Theta-functies gtt Functions, Theta Geometric quantization Quantum field theory Thetafunktion (DE-588)4185175-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd |
| topic_facet | Kwantumveldentheorie Theta-functies Functions, Theta Geometric quantization Quantum field theory Thetafunktion Quantenfeldtheorie Geometrische Quantisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013834178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007928388 |
| work_keys_str_mv | AT tjurinandrejn quantizationclassicalandquantumfieldtheoryandthetafunctions |