Integrability, self-duality, and twistor theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1996
|
| Series: | London Mathematical Society: London Mathematical Society monographs / New series
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 364 S. graph. Darst. |
| ISBN: | 0198534981 |
Staff View
MARC
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| 100 | 1 | |a Mason, Lionel J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integrability, self-duality, and twistor theory |c L. J. Mason and N. M. J. Woodhouse |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1996 | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1.1 Examples of integrability 1
1.2 Outline of the book 7
Notes on Chapter 1 9
I Reductions of the ASDYM equation
2 Mathematical background I 13
2.1 Gauge theories 13
2.2 Space time 14
2.3 Differential forms 16
2.4 Conformal transformations and compactified space time 19
2.5 Bundles, connections, and curvature 23
2.6 The Yang Mills equations 29
Notes on Chapter 2 30
3 The ASD Yang Mills equation 32
3.1 ASD electromagnetic fields 32
3.2 Lax pairs 33
3.3 Yang s equation and the if matrix 34
3.4 Lagrangians for the ASDYM equation 36
3.5 The Hamiltonian formalism 38
Notes on Chapter 3 42
4 Reduction of the ASDYM equation 43
4.1 Classification of reductions 43
4.2 Reductions of the linear ASD equation 45
4.3 Conformal reduction in the non Abelian case 46
4.4 Invariant connections and Higgs fields 47
4.5 The space of orbits 49
4.6 Backlund transformations 55
Notes on Chapter 4 56
5 Reduction to three dimensions 59
5.1 The Bogomolny equation 59
5.2 Hyperbolic monopoles and other generalizations 60
5.3 Reduction by a null translation 63
viii Contents
Notes on Chapter 5 66
6 Reduction to two dimensions 67
6.1 Two dimensional groups of conformal motions 67
6.2 Reductions by H++ 68
6.3 Reduction by H+o 73
6.4 Reduction by HSd 82
6.5 Reduction by Hasd 84
6.6 The Ernst equation 84
6.7 Reduction of Yang s equation 89
6.8 Liouville s equation 91
Notes on Chapter 6 92
7 Reductions to one dimension 95
7.1 Abelian reduction to one dimension 95
7.2 Nahm s equations and tops 98
7.3 The motion of an n dimensional rigid body 101
7.4 The Painleve equations 102
7.5 Non Abelian reductions 108
Notes on Chapter 7 109
8 Hierarchies 111
8.1 The KdV flows 111
8.2 The recursion operator for the ASDYM equation 114
8.3 Hamiltonian formalism 115
8.4 ASDYM and Bogomolny hierarchies 118
8.5 Reductions of the ASDYM flows 123
8.6 The generalized ASDYM equation 127
Notes on Chapter 8 132
II TWISTOR METHODS
9 Mathematical background II 137
9.1 Projective spaces and flag manifolds 137
9.2 Twistor space 138
9.3 Birkhoff s factorization theorem 145
9.4 Holomorphic vector bundles: the Cech description 149
9.5 9 operators 153
9.6 Cohomology 155
9.7 The Grassmannian 157
9.8 Scattering on the real line 158
9.9 Spinors 160
Notes on Chapter 9 168
Contents [x
10 The twistor correspondence 171
10.1 The concrete form of the Penrose Ward transform 171
10.2 The abstract form of the transform 176
10.3 The Painleve property 179
10.4 Global solutions in Euclidean signature 180
10.5 Global solutions in ultrahyperbolic signature 187
10.6 The GASDYM equation 194
10.7 The truncated GASDYM hierarchy 195
10.8 The linear Penrose transform 196
Notes on Chapter 10 201
11 Reductions of the Penrose Ward transform 204
11.1 Symmetries of the twistor correspondence 205
11.2 Symmetries of the twistor bundle 206
11.3 Reduced twistor spaces 211
11.4 The KdV and NLS equations 218
11.5 The initial value problem and inverse scattering 220
11.6 Isomonodromy and the Painleve equations 231
11.7 The Schlesinger equation 239
Notes on Chapter 11 241
12 Twistor construction of hierarchies 244
12.1 Transformations of the patching matrix 245
12.2 DS operators and the GASDYM hierarchy 250
12.3 The twistor construction of the DS flows 254
12.4 Explicit construction of solutions from twistor data 264
12.5 Hamiltonian formalism 269
12.6 The KP equation and the KP hierarchy 274
Notes on Chapter 12 282
13 ASD metrics 284
13.1 Self duality in curved space time 284
13.2 The Levi Civita connection 286
13.3 Spinors and the correspondence space 289
13.4 ASD conformal structures 294
13.5 Curved twistor spaces 300
13.6 Reductions 305
13.7 ASDYM fields and the switch map 307
Notes on Chapter 13 316
A Active and passive gauge transformations 317
B The Drinfeld Sokolov construction 319
Notes on Appendix B 326
x Contents
C Poisson and symplectic structures 328
Notes on Appendix C 338
D Reductions of the ASDYM equation 339
References 343
A note on notation 356
Index of notation 357
Index 359
|
| any_adam_object | 1 |
| author | Mason, Lionel J. Woodhouse, Nicholas M. J. 1949- |
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| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:00:23Z |
| institution | BVB |
| isbn | 0198534981 |
| language | English |
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| series2 | London Mathematical Society: London Mathematical Society monographs / New series |
| spelling | Mason, Lionel J. Verfasser aut Integrability, self-duality, and twistor theory L. J. Mason and N. M. J. Woodhouse Oxford Clarendon Press 1996 X, 364 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society monographs / New series 15 Integraltransformation (DE-588)4027235-7 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf Selbstdualität (DE-588)4180824-1 gnd rswk-swf Twistor (DE-588)4186504-2 gnd rswk-swf Twistor (DE-588)4186504-2 s Feldtheorie (DE-588)4016698-3 s Selbstdualität (DE-588)4180824-1 s DE-604 Integraltransformation (DE-588)4027235-7 s Woodhouse, Nicholas M. J. 1949- Verfasser (DE-588)142380253 aut New series London Mathematical Society: London Mathematical Society monographs 15 (DE-604)BV045355493 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007271252&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mason, Lionel J. Woodhouse, Nicholas M. J. 1949- Integrability, self-duality, and twistor theory Integraltransformation (DE-588)4027235-7 gnd Feldtheorie (DE-588)4016698-3 gnd Selbstdualität (DE-588)4180824-1 gnd Twistor (DE-588)4186504-2 gnd |
| subject_GND | (DE-588)4027235-7 (DE-588)4016698-3 (DE-588)4180824-1 (DE-588)4186504-2 |
| title | Integrability, self-duality, and twistor theory |
| title_auth | Integrability, self-duality, and twistor theory |
| title_exact_search | Integrability, self-duality, and twistor theory |
| title_full | Integrability, self-duality, and twistor theory L. J. Mason and N. M. J. Woodhouse |
| title_fullStr | Integrability, self-duality, and twistor theory L. J. Mason and N. M. J. Woodhouse |
| title_full_unstemmed | Integrability, self-duality, and twistor theory L. J. Mason and N. M. J. Woodhouse |
| title_short | Integrability, self-duality, and twistor theory |
| title_sort | integrability self duality and twistor theory |
| topic | Integraltransformation (DE-588)4027235-7 gnd Feldtheorie (DE-588)4016698-3 gnd Selbstdualität (DE-588)4180824-1 gnd Twistor (DE-588)4186504-2 gnd |
| topic_facet | Integraltransformation Feldtheorie Selbstdualität Twistor |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007271252&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045355493 |
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