Topology, geometry, and Gauge fields: foundations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2011
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Texts in applied mathematics
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XX, 437 S. graph. Darst. |
| ISBN: | 9781441972538 |
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| 100 | 1 | |a Naber, Gregory L. |d 1948- |e Verfasser |0 (DE-588)113221207 |4 aut | |
| 245 | 1 | 0 | |a Topology, geometry, and Gauge fields |b foundations |c Gregory L. Naber |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2011 | |
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| 490 | 1 | |a Texts in applied mathematics |v 25 | |
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Datensatz im Suchindex
| _version_ | 1804143554461696000 |
|---|---|
| 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
DI*ERENTIAL FORMS AND INTEGRATION
. . . . . . . . . . . . . . . . . . . . . . . . . . . 179
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 179
4.1 MULTILINEAR ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 179
4.2 VECTOR-VALUED FORMS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 198
4.3 DI*ERENTIAL 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
|
| any_adam_object | 1 |
| author | Naber, Gregory L. 1948- |
| author_GND | (DE-588)113221207 |
| author_facet | Naber, Gregory L. 1948- |
| author_role | aut |
| author_sort | Naber, Gregory L. 1948- |
| author_variant | g l n gl gln |
| building | Verbundindex |
| bvnumber | BV036856999 |
| classification_rvk | SK 280 SK 350 SK 950 UO 4060 |
| classification_tum | MAT 550f PHY 014f PHY 417f MAT 530f |
| ctrlnum | (OCoLC)706942307 (DE-599)BVBBV036856999 |
| dewey-full | 510 530.154 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 530 - Physics |
| dewey-raw | 510 530.154 |
| dewey-search | 510 530.154 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics 530 - Physics |
| discipline | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV036856999 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:49:30Z |
| institution | BVB |
| isbn | 9781441972538 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020772849 |
| oclc_num | 706942307 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM DE-11 DE-188 DE-83 |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-11 DE-188 DE-83 |
| physical | XX, 437 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| 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 |