Holdings: Topology and geometry for physics

Topology and geometry for physics:

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Bibliographic Details
Main Author:	Eschrig, Helmut 1942-2012 (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2011
Series:	Lecture notes in physics 822
Subjects:	Differentialgeometrie Mathematische Physik Topologie
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	XII, 389 S. graph. Darst.
ISBN:	9783642146992 9783642147005

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MARC


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Record in the Search Index

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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
any_adam_object	1
author	Eschrig, Helmut 1942-2012
author_GND	(DE-588)128424389
author_facet	Eschrig, Helmut 1942-2012
author_role	aut
author_sort	Eschrig, Helmut 1942-2012
author_variant	h e he
building	Verbundindex
bvnumber	BV036752095
classification_rvk	SK 280 SK 350 UD 8220
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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language	English
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physical	XII, 389 S. graph. Darst.
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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
url	http://deposit.dnb.de/cgi-bin/dokserv?id=3499263&prov=M&dok_var=1&dok_ext=htm 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
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work_keys_str_mv	AT eschrighelmut topologyandgeometryforphysics

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