Spinors in Four-Dimensional Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, MA
Birkhäuser
2010
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Progress in Mathematical Physics
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | VIII, 177 S. 235 mm x 155 mm |
| ISBN: | 9780817649838 9780817649845 |
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Datensatz im Suchindex
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|---|---|
| adam_text |
IMAGE 1
CONTENTS
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . V
1 SPINOR ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 1
1.1 ORTHOGONAL GROUPS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 2
1.2 NULL TETRADS AND THE SPINOR EQUIVALENT OF A TENSOR . . . . . . . . .
. . . . . 4
1.3 SPINORIAL REPRESENTATION OF THE ORTHOGONAL TRANSFORMATIONS . . . . .
. 17 1.3.1 EUCLIDEAN SIGNATURE . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 21
1.3.2 LORENTZIAN SIGNATURE . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 29
1.3.3 ULTRAHYPERBOLIC SIGNATURE . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 39
1.4 REFLECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 45
1.5 CLIFFORD ALGEBRA. DIRAC SPINORS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 49
1.6 INNER PRODUCTS. MATE OF A SPINOR . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 57
1.7 PRINCIPAL SPINORS. ALGEBRAIC CLASSIFICATION . . . . . . . . . . . .
. . . . . . . . . 59
EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 64
2 CONNECTION AND CURVATURE . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 67
2.1 COVARIANT DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 67
2.2 CURVATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 77
2.2.1 CURVATURE SPINORS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 78
2.2.2 ALGEBRAIC CLASSIFICATION OF THE CONFORMAL CURVATURE . . . . . . .
91 2.3 CONFORMAL RESCALINGS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 93
2.4 KILLING VECTORS. LIE DERIVATIVE OF SPINORS . . . . . . . . . . . . .
. . . . . . . . . 95
EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 99
3 APPLICATIONS TO GENERAL RELATIVITY . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 103
3.1 MAXWELL'S EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 104
3.2 DIRAC'S EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 115
3.3 EINSTEIN'S EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 122
3.3.1 THE GOLDBERG-SACHS THEOREM . . . . . . . . . . . . . . . . . . . .
. . . . . 123
3.3.2 SPACE-TIMES WITH SYMMETRIES. ERNST POTENTIALS . . . . . . . . . .
. 131 3.4 KILLING SPINORS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 137
EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 144
VII
IMAGE 2
VIII CONTENTS
4 FURTHER APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 149
4.1 SELF-DUAL YANG-MILLS FIELDS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 149
4.2 H AND H H SPACES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 152
4.3 KILLING BISPINORS. THE DIRAC OPERATOR . . . . . . . . . . . . . . .
. . . . . . . . . . 162
EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 165
A BASES INDUCED BY COORDINATE SYSTEMS . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 167
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 171
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 |
| any_adam_object | 1 |
| author | Torres del Castillo, Gerardo F. 1956- |
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| bvnumber | BV036666215 |
| classification_rvk | SK 370 |
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| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| series | Progress in Mathematical Physics |
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| spelling | Torres del Castillo, Gerardo F. 1956- Verfasser (DE-588)140987932 aut Spinors in Four-Dimensional Spaces Gerardo F. Torres Castillo 1. Aufl. Cambridge, MA Birkhäuser 2010 VIII, 177 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Progress in Mathematical Physics 59 Vierdimensionaler Raum (DE-588)4138351-5 gnd rswk-swf Spinoranalysis (DE-588)4182329-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Spinoranalysis (DE-588)4182329-1 s Vierdimensionaler Raum (DE-588)4138351-5 s Topologische Gruppe (DE-588)4135793-0 s Mathematische Physik (DE-588)4037952-8 s DE-604 Progress in Mathematical Physics 59 (DE-604)BV013823265 59 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3439878&prov=M&dok_var=1&dok_ext=htm Inhaltstext SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020585406&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Torres del Castillo, Gerardo F. 1956- Spinors in Four-Dimensional Spaces Progress in Mathematical Physics Vierdimensionaler Raum (DE-588)4138351-5 gnd Spinoranalysis (DE-588)4182329-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4138351-5 (DE-588)4182329-1 (DE-588)4037952-8 (DE-588)4135793-0 |
| title | Spinors in Four-Dimensional Spaces |
| title_auth | Spinors in Four-Dimensional Spaces |
| title_exact_search | Spinors in Four-Dimensional Spaces |
| title_full | Spinors in Four-Dimensional Spaces Gerardo F. Torres Castillo |
| title_fullStr | Spinors in Four-Dimensional Spaces Gerardo F. Torres Castillo |
| title_full_unstemmed | Spinors in Four-Dimensional Spaces Gerardo F. Torres Castillo |
| title_short | Spinors in Four-Dimensional Spaces |
| title_sort | spinors in four dimensional spaces |
| topic | Vierdimensionaler Raum (DE-588)4138351-5 gnd Spinoranalysis (DE-588)4182329-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Vierdimensionaler Raum Spinoranalysis Mathematische Physik Topologische Gruppe |
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