Holdings: Topology, geometry, and Gauge fields

Topology, geometry, and Gauge fields: foundations

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Bibliographic Details
Main Author:	Naber, Gregory L. 1948- (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 2011
Edition:	2. ed.
Series:	Texts in applied mathematics 25
Subjects:	Eichtheorie Topologie Mathematische Physik Eichfeld Geometrie
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XX, 437 S. graph. Darst.
ISBN:	9781441972538

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Record in the Search Index

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adam_text	CONTENTS CHAPTER 1 GEOMETRICAL BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 SMOOTH MANIFOLDS AND MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 MATRIX LIE GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 PRINCIPAL BUNDLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4 CONNECTIONS AND CURVATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5 ASSOCIATED BUNDLES AND MATTER FIELDS . . . . . . . . . . . . . . . . . . . . . . 38 CHAPTER 2 PHYSICAL MOTIVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.1 GENERAL FRAMEWORK FOR CLASSICAL GAUGE THEORIES . . . . . . . . . . . . 45 2.2 ELECTROMAGNETIC FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3 SPIN ZERO ELECTRODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.4 SPIN ONE-HALF ELECTRODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.5 S U (2) -YANG-MILLS-HIGGS THEORY ON R N . . . . . . . . . . . . . . . . . . . . . 104 2.6 EPILOGUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 CHAPTER 3 FRAME BUNDLES AND SPACETIMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.1 PARTITIONS OF UNITY, RIEMANNIAN METRICS AND CONNECTIONS . . . . . 139 3.2 CONTINUOUS VERSUS SMOOTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 3.3 FRAME BUNDLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 3.4 MINKOWSKI SPACETIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 3.5 SPACETIME MANIFOLDS AND SPINOR STRUCTURES . . . . . . . . . . . . . . . . . 168 CHAPTER 4 DIERENTIAL FORMS AND INTEGRATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 4.1 MULTILINEAR ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 4.2 VECTOR-VALUED FORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 4.3 DIERENTIAL FORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 4.4 THE DE RHAM COMPLEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 4.5 TENSORIAL FORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 4.6 INTEGRATION ON MANIFOLDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 4.7 STOKES THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 CHAPTER 5 DE RHAM COHOMOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 5.1 THE DE RHAM COHOMOLOGY GROUPS . . . . . . . . . . . . . . . . . . . . . . . . 258 5.2 INDUCED HOMOMORPHISMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 5.3 COCHAIN COMPLEXES AND THEIR COHOMOLOGY . . . . . . . . . . . . . . . . . 275 5.4 THE MAYER-VIETORIS SEQUENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 XI XII CONTENTS 5.5 THE COHOMOLOGY OF COMPACT, ORIENTABLE MANIFOLDS . . . . . . . . . . 290 5.6 THE BROUWER DEGREE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 5.7 THE HOPF INVARIANT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 CHAPTER 6 CHARACTERISTIC CLASSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 6.1 MOTIVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 6.2 ALGEBRAIC PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 6.3 THE CHERN-WEIL HOMOMORPHISM . . . . . . . . . . . . . . . . . . . . . . . . . . 317 6.4 CHERN NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 6.5 Z 2 - * C ECH COHOMOLOGY FOR SMOOTH MANIFOLDS . . . . . . . . . . . . . . . . . 335 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 SEIBERG-WITTEN GAUGE THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 A.1 DONALDSON INVARIANTS AND TQFT . . . . . . . . . . . . . . . . . . . . . . . . . . 351 A.2 CLI*ORD ALGEBRA AND SPIN C -STRUCTURES . . . . . . . . . . . . . . . . . . . . . . 363 A.3 SEIBERG-WITTEN EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 A.4 THE MODULI SPACE AND INVARIANT . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 A.5 THE WITTEN CONJECTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
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spelling	Naber, Gregory L. 1948- Verfasser (DE-588)113221207 aut Topology, geometry, and Gauge fields foundations Gregory L. Naber 2. ed. New York [u.a.] Springer 2011 XX, 437 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 25 Hier auch später erschienene, unveränderte Nachdrucke Eichtheorie (DE-588)4122125-4 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Eichfeld (DE-588)4328765-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Eichfeld (DE-588)4328765-7 s Topologie (DE-588)4060425-1 s Geometrie (DE-588)4020236-7 s DE-604 Eichtheorie (DE-588)4122125-4 s Mathematische Physik (DE-588)4037952-8 s Erscheint auch als Online-Ausgabe 978-1-4419-7254-5 Erscheint auch als Druck-Ausgabe, Paperback 978-1-4614-2682-0 Texts in applied mathematics 25 (DE-604)BV002476038 25 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020772849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Naber, Gregory L. 1948- Topology, geometry, and Gauge fields foundations Texts in applied mathematics Eichtheorie (DE-588)4122125-4 gnd Topologie (DE-588)4060425-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Eichfeld (DE-588)4328765-7 gnd Geometrie (DE-588)4020236-7 gnd
subject_GND	(DE-588)4122125-4 (DE-588)4060425-1 (DE-588)4037952-8 (DE-588)4328765-7 (DE-588)4020236-7
title	Topology, geometry, and Gauge fields foundations
title_auth	Topology, geometry, and Gauge fields foundations
title_exact_search	Topology, geometry, and Gauge fields foundations
title_full	Topology, geometry, and Gauge fields foundations Gregory L. Naber
title_fullStr	Topology, geometry, and Gauge fields foundations Gregory L. Naber
title_full_unstemmed	Topology, geometry, and Gauge fields foundations Gregory L. Naber
title_short	Topology, geometry, and Gauge fields
title_sort	topology geometry and gauge fields foundations
title_sub	foundations
topic	Eichtheorie (DE-588)4122125-4 gnd Topologie (DE-588)4060425-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Eichfeld (DE-588)4328765-7 gnd Geometrie (DE-588)4020236-7 gnd
topic_facet	Eichtheorie Topologie Mathematische Physik Eichfeld Geometrie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020772849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV002476038
work_keys_str_mv	AT nabergregoryl topologygeometryandgaugefieldsfoundations

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