Topology and geometry for physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in physics
822 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XII, 389 S. graph. Darst. |
| ISBN: | 9783642146992 9783642147005 |
Internformat
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Datensatz im Suchindex
| _version_ | 1805094890091053056 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
REFERENCES 9
2 TOPOLOGY 11
2.1 BASIC DEFINITIONS 11
2.2 BASE OF TOPOLOGY, METRIC, NORM 13
2.3 DERIVATIVES 22
2.4 COMPACTNESS 29
2.5 CONNECTEDNESS, HOMOTOPY 38
2.6 TOPOLOGICAL CHARGES IN PHYSICS 48
REFERENCES 53
3 MANIFOLDS 55
3.1 CHARTS AND ATLASES 55
3.2 SMOOTH MANIFOLDS 58
3.3 TANGENT SPACES 60
3.4 VECTOR FIELDS 67
3.5 MAPPINGS OF MANIFOLDS, SUBMANIFOLDS 71
3.6 FROBENIUS' THEOREM 77
3.7 EXAMPLES FROM PHYSICS 82
3.7.1 CLASSICAL POINT MECHANICS 82
3.7.2 CLASSICAL AND QUANTUM MECHANICS 84
3.7.3 CLASSICAL POINT MECHANICS UNDER MOMENTUM CONSTRAINTS 86
3.7.4 CLASSICAL MECHANICS UNDER VELOCITY CONSTRAINTS 93 3.7.5
THERMODYNAMICS 94
REFERENCES 95
4 TENSOR FIELDS 97
4.1 TENSOR ALGEBRAS 97
4.2 EXTERIOR ALGEBRAS 102
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1004070764
DIGITALISIERT DURCH
IMAGE 2
LI CONTENTS
4.3 TENSOR FIELDS AND EXTERIOR FORMS 106
4.4 EXTERIOR DIFFERENTIAL CALCULUS 110
REFERENCES 114
INTEGRATION, HOMOLOGY AND COHOMOLOGY 115
5.1 PRELUDE IN EUCLIDEAN SPACE 115
5.2 CHAINS OF SIMPLICES 122
5.3 INTEGRATION OF DIFFERENTIAL FORMS 127
5.4 DE RHAM COHOMOLOGY 129
5.5 HOMOLOGY AND HOMOTOPY 135
5.6 HOMOLOGY AND COHOMOLOGY OF COMPLEXES 138
5.7 EULER'S CHARACTERISTIC 146
5.8 CRITICAL POINTS 148
5.9 EXAMPLES FROM PHYSICS 153
REFERENCES 171
LIE GROUPS 173
6.1 LIE GROUPS AND LIE ALGEBRAS 173
6.2 LIE GROUP HOMOMORPHISMS AND REPRESENTATIONS 177
6.3 LIE SUBGROUPS 179
6.4 SIMPLY CONNECTED COVERING GROUP 180
6.5 THE EXPONENTIAL MAPPING 188
6.6 THE GENERAL LINEAR GROUP GL(N,K) 190
6.7 EXAMPLE FROM PHYSICS: THE LORENTZ GROUP 197
6.8 THE ADJOINT REPRESENTATION 202
REFERENCES 204
BUNDLES AND CONNECTIONS 205
7.1 PRINCIPAL FIBER BUNDLES 206
7.2 FRAME BUNDLES 211
7.3 CONNECTIONS ON PRINCIPLE FIBER BUNDLES 213
7.4 PARALLEL TRANSPORT AND HOLONOMY 220
7.5 EXTERIOR COVARIANT DERIVATIVE AND CURVATURE FORM 222
7.6 FIBER BUNDLES 226
7.7 LINEAR AND AFFINE CONNECTIONS 231
7.8 CURVATURE AND TORSION TENSORS 238
7.9 EXPRESSIONS IN LOCAL COORDINATES ON M 240
REFERENCES 246
PARALLELISM, HOLONOMY, HOMOTOPY AND (CO)HOMOLOGY 247 8.1 THE EXACT
HOMOTOPY SEQUENCE 247
8.2 HOMOTOPY OF SECTIONS 253
8.3 GAUGE FIELDS AND CONNECTIONS ON R 4 256
8.4 GAUGE FIELDS AND CONNECTIONS ON MANIFOLDS 262
IMAGE 3
CONTENTS IX
8.5 CHARACTERISTIC CLASSES 270
8.6 GEOMETRIE PHASES IN QUANTUM PHYSICS 276
8.6.1 BERRY-SIMON CONNECTION 276
8.6.2 DEGENERATE CASE 278
8.6.3 ELECTRICAL POLARIZATION 281
8.6.4 ORBITAL MAGNETISM 289
8.6.5 TOPOLOGICAL INSULATORS 294
8.7 GAUGE FIELD THEORY OF MOLECULAR PHYSICS 296
REFERENCES 297
9 RIEMANNIAN GEOMETRY 299
9.1 RIEMANNIAN METRIC 300
9.2 HOMOGENEOUS MANIFOLDS 303
9.3 RIEMANNIAN CONNECTION 308
9.4 GEODESIC NORMAL COORDINATES 312
9.5 SECTIONAL CURVATURE 321
9.6 GRAVITATION 326
9.7 COMPLEX, HERMITIAN AND KAEHLERIAN MANIFOLDS 336
REFERENCES 346
COMPENDIUM 347
LIST OF SYMBOLS 379
INDEX 381 |
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| ctrlnum | (OCoLC)845801070 (DE-599)DNB1004070764 |
| dewey-full | 530.154 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.154 |
| dewey-search | 530.154 |
| dewey-sort | 3530.154 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| isbn | 9783642146992 9783642147005 |
| language | English |
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| physical | XII, 389 S. graph. Darst. |
| publishDate | 2011 |
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| spelling | Eschrig, Helmut 1942-2012 Verfasser (DE-588)128424389 aut Topology and geometry for physics Helmut Eschrig Berlin [u.a.] Springer 2011 XII, 389 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 822 Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Topologie (DE-588)4060425-1 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Lecture notes in physics 822 (DE-604)BV000003166 822 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3499263&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020669335&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eschrig, Helmut 1942-2012 Topology and geometry for physics Lecture notes in physics Differentialgeometrie (DE-588)4012248-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4037952-8 (DE-588)4060425-1 |
| title | Topology and geometry for physics |
| title_auth | Topology and geometry for physics |
| title_exact_search | Topology and geometry for physics |
| title_full | Topology and geometry for physics Helmut Eschrig |
| title_fullStr | Topology and geometry for physics Helmut Eschrig |
| title_full_unstemmed | Topology and geometry for physics Helmut Eschrig |
| title_short | Topology and geometry for physics |
| title_sort | topology and geometry for physics |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Differentialgeometrie Mathematische Physik Topologie |
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