Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ...:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1988
|
| Schriftenreihe: | World Scientific lecture notes in physics
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 325 - 345 |
| Beschreibung: | XII, 345 S. |
| ISBN: | 997150426X 9971504278 |
Internformat
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Datensatz im Suchindex
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| adam_text | ix
CONTENTS
Chapter 1 GENERALITIES 1
1.1 Introduction 1
1.2 Differentiable manifolds 6
1.3 Riemannian manifolds 8
1. Metrics, connections and curvatures 8
2. Particular spaces 12
Chapter 2 RIEMANNIAN GEOMETRY OF LIE GROUPS 15
2.0 Summary 16
2.1 The case of SU(2) 18
2.2 Left and right fundamental fields 25
2.3 Principal fibration of a group with respect to a subgroup 28
2.4 Bi invariant metrics 30
2.5 Left and right invariant metrics 32
2.6 Metrics with isometry group where H.K are subgroups of G 35
2.7 G x K invariant metrics related to a fibration of G 35
2.8 Dimensionally reducible metrics (action of a bundle of
groups) 36
2.9 Einstein metrics on groups 38
2.10 On the classification of compact simple Lie groups 41
2.11 Standard normalizations, indices etc. 42
2.12 Pointers to the literature 50
Chapter 3 RIEMANNIAN GEOMETRY OF HOMOGENEOUS SPACES 51
3.0 Summary 51
3.1 The example of S2 58
3.2 The role of the normalizer N of H in G 60
3.3 Fundalemtal fields 67
3.4 G invariant metrics on H G 70
3.5 Invariant metrics on H G related to the fibration of H G 78
3.6 Einstein metrics on homogeneous spaces 80
3.7 Pointers to the literature 83
X
Chapter 4 RIEMANNIAN GEOMETRY OF A (RIGHT) PRINCIPAL
BUNDLE 84
4.0 Summary 85
4.1 Example of MX SU (2) 91
4.2 Fundamental fields on P 92
4.3 Local product representation of P 93
4.4 G invariant metrics and the reduction theorem 95
4.5 Curvature of G invariant metrics on a principal bundle P 103
4.6 Action principle and the consistency requirement 105
4.7 Conformal rescaling and the effective Lagrangian 108
4.8 On the interpretation of the scalar fields. Physical units 111
4.9 Color charges, scalar charges and the particule trajectories 117
4.10 Generalised Kaluza Klein metrics (action of a bundle of
groups) 119
4.11 The group of automorphisms of a principal bundle 123
4.12 Pointers to the literature 130
Chapter 5 RIEMANNIAN GEOMETRY OF A BUNDLE WITH FIBERS
G/H AND A GIVEN ACTION OF A LIE GROUP G 131
5.0 Summary 132
5.1 The structure of a simple G space 139
5.2 Examples 144
5.3 Fundamental and invariant vector fields 148
5.4 G invariant metrics on E 152
5.5 Curvature tensors for G invariant metrics 160
5.6 Examples 163
5.7 Action principle and consistency requirement 170
5.8 Conformal rescaling and the effective lagrangian 173
5.9 Normalization and units, the potential for scalar fields 174
5.10 Color charges, scalar charges and the particle trajectories 179
5.11 Generalized Kaluza Klein metrics (action of a bundle of
groups) 181
5.12 Some complements on G spaces 183
5.13 Pointers to the literature 184
xi
Chapter 6 GEOMETRY OF MATTER FIELDS 185
6.0 Summary 185
6.1 Description of matter fields 189
6.2 Covariant derivative and curvature 192
6.3 The case of M endowed with affine connection and/or metric 197
6.4 The case of a bundle P = P(M,G) endowed with a principal
connection w and whose base is endowed with affine
connection 201
6.5 Spin structures and spinors 205
6.6 Generalized spin structures 212
6.7 An example: Einstein Cartan theory with spinor fields 214
6.8 Miscellaneous 219
6.9 Pointers to the literature 219
Chapter 7 HARMONIC ANALYSIS AND DIMENSIONAL REDUCTION 220
7.0 Summary 220
7.1 A particular case of 7.2: non abelian harmonic analysis 228
7.2 Harmonic expansion (generalised Peter Weyl theorem) 230
7.3 A particular case of 7.4: induced representations 234
7.4 Harmonic expansion —2— (generalised Frobenius theorem) 239
7.5 Harmonic expansion and dimensional reduction 243
7.6 Generalised homogeneous differential operators and the
consistency problem for matter fields 245
7.7 Pointers to the literature 247
Chapter 8 DIMENSIONAL REDUCTION OF THE ORTHOGONAL
BUNDLE AND OF THE SPIN BUNDLE 248
8.0 Summary 248
8.1 The space of adapted orthonormal frames 253
8.2 Dimensionally reduced Laplace Beltrami operators 261
8.3 Dimensional reduction of spinor fields 262
8.4 The spectrum of Laplace operator for G invariant metrics
on groups and homogeneous spaces 265
8.5 The spectrum of the Dirac operator for G invariant
metrics on groups and homogeneous spaces 274
8.6 Example of dimensional reduction of spinor fields 279
8.7 Pointers to the literature 280
xii
Chapter 9 G INVARIANCE OF EINSTEIN YANG MILLS SYSTEMS 281
9.0 Summary 281
9.1 Symmetries of a principal bundle 287
9.2 Reduction of the Einstein Yang Mills action 301
9.3 Examples and comments 311
9.4 Pointers to the literature 315
Chapter 10 ACTION OF A BUNDLE OF GROUPS 316
10.1 Motivations 316
10.2 Examples of dimensionally reducible metrics (but not
G invariant) 317
10.3 An extended Kaluza Klein scheme 320
BIBLIOGRAPHY AND REFERENCES 323
|
| any_adam_object | 1 |
| author | Coquereaux, Robert Jadcyzk, Arkadiusz |
| author_facet | Coquereaux, Robert Jadcyzk, Arkadiusz |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)17387323 (DE-599)BVBBV002213278 |
| dewey-full | 516.373 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.373 |
| dewey-search | 516.373 |
| dewey-sort | 3516.373 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV002213278 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:09Z |
| institution | BVB |
| isbn | 997150426X 9971504278 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001453656 |
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| physical | XII, 345 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
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| publisher | World Scientific |
| record_format | marc |
| series | World Scientific lecture notes in physics |
| series2 | World Scientific lecture notes in physics |
| spelling | Coquereaux, Robert Verfasser aut Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... Robert Coquereaux ; Arkadiusz Jadcyzk Singapore [u.a.] World Scientific 1988 XII, 345 S. txt rdacontent n rdamedia nc rdacarrier World Scientific lecture notes in physics 16 Literaturverz. S. 325 - 345 Faisceaux fibrés (Mathématiques) Fibrés vectoriels Riemann, Géométrie de Riemann-ruimten gtt Fiber bundles (Mathematics) Geometry, Riemannian Kaluza-Klein theories Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Dimensionsreduktion (DE-588)4224279-4 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Faserbündel (DE-588)4135582-9 gnd rswk-swf Kaluza-Klein-Theorie (DE-588)4224276-9 gnd rswk-swf Faserbündel <Mathematik> gnd rswk-swf Dimensionsreduktion (DE-588)4224279-4 s DE-604 Faserbündel (DE-588)4135582-9 s Riemannsche Geometrie (DE-588)4128462-8 s Gruppe Mathematik (DE-588)4022379-6 s Kaluza-Klein-Theorie (DE-588)4224276-9 s Faserbündel <Mathematik> f Jadcyzk, Arkadiusz Verfasser aut World Scientific lecture notes in physics 16 (DE-604)BV000819327 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001453656&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Coquereaux, Robert Jadcyzk, Arkadiusz Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... World Scientific lecture notes in physics Faisceaux fibrés (Mathématiques) Fibrés vectoriels Riemann, Géométrie de Riemann-ruimten gtt Fiber bundles (Mathematics) Geometry, Riemannian Kaluza-Klein theories Riemannsche Geometrie (DE-588)4128462-8 gnd Dimensionsreduktion (DE-588)4224279-4 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Faserbündel (DE-588)4135582-9 gnd Kaluza-Klein-Theorie (DE-588)4224276-9 gnd |
| subject_GND | (DE-588)4128462-8 (DE-588)4224279-4 (DE-588)4022379-6 (DE-588)4135582-9 (DE-588)4224276-9 |
| title | Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... |
| title_auth | Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... |
| title_exact_search | Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... |
| title_full | Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... Robert Coquereaux ; Arkadiusz Jadcyzk |
| title_fullStr | Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... Robert Coquereaux ; Arkadiusz Jadcyzk |
| title_full_unstemmed | Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... Robert Coquereaux ; Arkadiusz Jadcyzk |
| title_short | Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... |
| title_sort | riemannian geometry fiber bundles kaluza klein theories and all that |
| topic | Faisceaux fibrés (Mathématiques) Fibrés vectoriels Riemann, Géométrie de Riemann-ruimten gtt Fiber bundles (Mathematics) Geometry, Riemannian Kaluza-Klein theories Riemannsche Geometrie (DE-588)4128462-8 gnd Dimensionsreduktion (DE-588)4224279-4 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Faserbündel (DE-588)4135582-9 gnd Kaluza-Klein-Theorie (DE-588)4224276-9 gnd |
| topic_facet | Faisceaux fibrés (Mathématiques) Fibrés vectoriels Riemann, Géométrie de Riemann-ruimten Fiber bundles (Mathematics) Geometry, Riemannian Kaluza-Klein theories Riemannsche Geometrie Dimensionsreduktion Gruppe Mathematik Faserbündel Kaluza-Klein-Theorie Faserbündel <Mathematik> |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001453656&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000819327 |
| work_keys_str_mv | AT coquereauxrobert riemanniangeometryfiberbundleskaluzakleintheoriesandallthat AT jadcyzkarkadiusz riemanniangeometryfiberbundleskaluzakleintheoriesandallthat |