Supersymmetric Killing structures:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
2003
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Leipzig, Univ., Diss., 2003 |
| Beschreibung: | II, 116 S. 30 cm |
Internformat
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Datensatz im Suchindex
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1
CONTENTS
PREFACE 1
INTRODUCTION. 1
CONVENTIONS AND BASIC MATERIAL. 4
1 REAL AND COMPLEX SPIN GEOMETRY 9
1.1 BASIC PROPERTIES OF COMPLEX AND REAL SPIN-REPRESENTATIONS. 9
1.2 TRANSFORMATIONS OF THE CLIFFORD-REPRESENTATIONS. 11
1.3 THE REAL SPINORS. 13
2 SUPERSYMMETRY 15
2.1 THE CLASSICAL SUPERSYMMETRY ALGEBRA. 15
2.2 COMPLEX SUPERSYMMETRY. 17
2.3 REAL SUPERSYMMETRY. 17
2.4 EXAMPLE: THE FOUR DIMENSIONAL EUCLIDEAN SPACE. 21
2.A INDEPENDENCE PROPERTIES OF THE MORPHISMS . 23
2.B SUPERSYMMETRY FROM CHARGE CONJUGATION. 25
3 THE SPECIAL GRADED MANIFOLD 28
3.1 GRADED MANIFOLDS. 28
3.1.1 DERIVATIONS. 29
3.2 THE DEFINITION OF THE SPECIAL GRADED MANIFOLD. 29
3.3 THE SHEAF OF FUNCTIONS. 32
3.4 THE NATURAL BILINEAR FORM ON THE SGM. 34
3.5 NATURAL FIELDS ON THE SGM. 35
3.5.1 ENDOMORPHISMS AS FIELDS, FIELDS OF ENDOMORPHISMS. 36
4 THE EVEN KILLING FIELDS ON THE SPECIAL GRADED MANIFOLD 39
5 SUPERSYMMETRIC KILLING STRUCTURES 45
5.1 SUPERSYMMETRIC KILLING STRUCTURES. 45
5.2 THE ODD FIELDS.
46
5.2.1 THE ODD ANSATZ. 46
5.2.2 THE ODD-ODD COMMUTATOR. 47
5.3 THE EVEN-ODD COMMUTATOR . 48
5.4 ODD KILLING FIELDS AND A FIRST EXAMPLE. 49
5.5 THE THIRD ORDER TERM. 50
5.5.1 BASIC PROPERTIES. 50
5.5.2 COMMUTATOR IDENTITIES AND SYMMETRIES. 53
5.A THE SYMMETRIZATIONS OF R . 57
6 SSKS ON MANIFOLDS WITH SPECIAL HOLONOMY 59
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/968625061
11
6.1 THE THIRD ORDER TERM IN COMPLEX COORDINATES. 60
6.2 THE REAL SSKS IN THE SU(N) CASE. 61
6.3 THE COMPLEX SSKS IN THE SU(N) CASE. 65
6.4 THE CASE OF DIMENSION D = 4. 66
6.4.1 THE EGUCHI HANSON METRIC. 66
6.4.2 THE GENERALIZATION. 74
6.5 THE CASE OF SPIN(7) AND G
2
MANIFOLDS. 74
6.5.1 THE SSKS IN THE SPIN(7) CASE. 77
6.A THE THIRD ORDER TERM IN THE QUATERNIONIC CASE. 78
6.B REMARKS ON THE REPRESENTATIONS OF SPIN(7) AND G
2
. 79
7 BRINKMANN SPACES WITH FINITE SSKS 84
7.1 PP-WAVES. 84
7.2 GENERAL BRINKMANN SPACES. 86
8 THE CENTRAL PART OF THE SSKS 89
8.1 THE GENERAL FORM OF THE SSKS. 89
8.2 THE PROOFS . 91
9 SSKS ON PRODUCTS OF MANIFOLDS 93
9.1 THE SPIN REPRESENTATION FOR PRODUCTS OF RIEMANNIAN MANIFOLDS. 93
9.2 REMARKS ON THE SSKS ON PRODUCTS OF MANIFOLDS . 99
10 FURTHER REMARKS 104
10.1 INTRODUCING TWISTOR SPINORS. 104
10.2 THE COMMUTATOR FOR THE MODIFIED ODD ANSATZ. 107
10.3 OUTLOOK. 112
REFERENCES
113 |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-22T17:38:21Z |
| institution | BVB |
| language | English |
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| physical | II, 116 S. 30 cm |
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| spelling | Klinker, Frank 1973- Verfasser (DE-588)124933904 aut Supersymmetric Killing structures vorgelegt von Frank Klinker 2003 II, 116 S. 30 cm txt rdacontent n rdamedia nc rdacarrier Leipzig, Univ., Diss., 2003 Supersymmetrie - Supermannigfaltigkeit - Lie-Algebra - Superalgebra - Killingsches Vektorfeld Supersymmetrie (DE-588)4128574-8 gnd rswk-swf Superalgebra (DE-588)4304028-7 gnd rswk-swf Supermannigfaltigkeit (DE-588)4289285-5 gnd rswk-swf Killingsches Vektorfeld (DE-588)4163778-1 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Supersymmetrie (DE-588)4128574-8 s Supermannigfaltigkeit (DE-588)4289285-5 s Lie-Algebra (DE-588)4130355-6 s Superalgebra (DE-588)4304028-7 s Killingsches Vektorfeld (DE-588)4163778-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010562722&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klinker, Frank 1973- Supersymmetric Killing structures Supersymmetrie - Supermannigfaltigkeit - Lie-Algebra - Superalgebra - Killingsches Vektorfeld Supersymmetrie (DE-588)4128574-8 gnd Superalgebra (DE-588)4304028-7 gnd Supermannigfaltigkeit (DE-588)4289285-5 gnd Killingsches Vektorfeld (DE-588)4163778-1 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4128574-8 (DE-588)4304028-7 (DE-588)4289285-5 (DE-588)4163778-1 (DE-588)4130355-6 (DE-588)4113937-9 |
| title | Supersymmetric Killing structures |
| title_auth | Supersymmetric Killing structures |
| title_exact_search | Supersymmetric Killing structures |
| title_full | Supersymmetric Killing structures vorgelegt von Frank Klinker |
| title_fullStr | Supersymmetric Killing structures vorgelegt von Frank Klinker |
| title_full_unstemmed | Supersymmetric Killing structures vorgelegt von Frank Klinker |
| title_short | Supersymmetric Killing structures |
| title_sort | supersymmetric killing structures |
| topic | Supersymmetrie - Supermannigfaltigkeit - Lie-Algebra - Superalgebra - Killingsches Vektorfeld Supersymmetrie (DE-588)4128574-8 gnd Superalgebra (DE-588)4304028-7 gnd Supermannigfaltigkeit (DE-588)4289285-5 gnd Killingsches Vektorfeld (DE-588)4163778-1 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Supersymmetrie - Supermannigfaltigkeit - Lie-Algebra - Superalgebra - Killingsches Vektorfeld Supersymmetrie Superalgebra Supermannigfaltigkeit Killingsches Vektorfeld Lie-Algebra Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010562722&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT klinkerfrank supersymmetrickillingstructures |