Orthogonal and symplectic Clifford algebras: spinor structures
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1990
|
| Series: | Mathematics and its applications
57 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 350 S. |
| ISBN: | 0792305418 |
Staff View
MARC
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| 100 | 1 | |a Crumeyrolle, Albert |d 1919-1992 |e Verfasser |0 (DE-588)119356104 |4 aut | |
| 245 | 1 | 0 | |a Orthogonal and symplectic Clifford algebras |b spinor structures |c by Albert Crumeyrolle |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1990 | |
| 300 | |a XIII, 350 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 57 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction. xi
1 Orthogonal and symplectic geometries. 1
1.1 Background on bilinear forms 1
1.2 Common properties of the orthogonal and the symplectic geometries. 5
1.3 Special properties of the orthogonal geometry 13
1.4 Special properties of the symplectic geometry 17
1.5 Selected references 20
2 Tensor algebras, exterior algebras and symmetric algebras. 21
2.1 Background on tensor algebras 21
2.2 Essential properties of exterior algebras 24
2.3 Essential properties of symmetric algebras 32
2.4 The inner product and the annihilation operators 33
2.5 Selected references 36
3 Orthogonal Clifford algebras. 37
3.1 Definition and general properties 37
3.2 Real and complex Clifford algebras : the periodicity theorems . ... 46
3.3 The direct study of the Clifford algebra structure 50
3.4 Selected references 57
4 The Clifford groups, the twisted Clifford groups and their funda¬
mental subgroups. 58
4.1 Clifford groups 58
4.2 Twisted Clifford groups or Clifford a groups 61
4.3 Degenerate Clifford groups 64
4.4 Selected references 66
5 Spinors and spin representations. 68
5.1 Notions on the representations of associative algebras and on semi
simple rings 68
5.2 Spin representations 76
5.3 Selected references 84
viii CONTENTS
6 Fundamental Lie algebras and Lie groups in the Clifford algebras. 85
6.1 The exponential function in the Clifford algebras 85
6.2 Connectedness 90
6.3 Selected references 93
7 The matrix approach to the spinors in three and four dimensional
spaces. 94
7.1 The complex Clifford algebra in C3 95
7.2 Minkowski Clifford algebras and Dirac matrices 97
7.3 Selected references 102
8 The spinors in maximal index and even dimension. 103
8.1 Pure spinors and associated m.t.i.s 103
8.2 Invariant bilinear forms on the spinor space 110
8.3 The tensor product of a spin representation with itself or with its dual. 113
8.4 Selected references 117
9 The spinors in maximal index and odd dimension. 118
9.1 Standard spinors 118
9.2 M.t.i.s. and pure spinors 119
10 The hermitian structure on the space of complex spinors—conju¬
gations and related notions. 122
10.1 Some background and preliminary results 122
10.2 The fundamental hermitian sesquilinear form. Special cases 124
10.3 Hermitian sesquilinear forms and conjugations. The general case, n =
2r 127
10.4 Invariant hermitian sesquilinear forms 141
10.5 Conjugations and hermitian sesquilinear forms if n = 2r + 1 142
10.6 Selected references 144
11 Spinoriality groups. 145
11.1 145
11.2 Selected references 148
12 Coverings of the complete conformal group—twistors. 149
12.1 The complete conformal group 149
12.2 Coverings of the complete conformal group 150
12.3 Twistors 155
12.4 Selected references 164
CONTENTS ix
13 The triality principle, the interaction principle and orthosymplectic
graded Lie algebras. 165
13.1 E. Cartan s triality principle 165
13.2 The generalized triality principle 168
13.3 Selected references 178
14 The Clifford algebra and the Clifford bundle of a pseudo riemannian
manifold. Existence conditions for spinor structures. 180
14.1 The Clifford algebra of a manifold 180
14.2 Existence conditions for spinor structures 184
14.3 Some particular results 190
14.4 Enlarged spinor structures and others 194
14.5 Spinor structures in the odd dimensional case 197
14.6 Spinor structures on spheres and on projective spaces 197
15 Spin derivations. 204
15.1 Spin connections—covariant derivation 204
15.2 The Lie derivative of spinors 216
16 The Dirac equation. 219
16.1 219
16.2 The Dirac equation and the associated quantities 220
16.3 Selected references 232
17 Symplectic Clifford algebras and associated groups. 233
17.1 Common symplectic Clifford algebras or Weyl algebras 233
17.2 Enlarged symplectic Clifford algebras 238
18 Symplectic spinor bundles—the Maslov index. 256
18.1 The symplectic Clifford bundle of an almost symplectic manifold. . . 256
18.2 The three sided inertial cocycle and the Maslov index 259
18.3 Selected references 266
19 Algebra deformations on symplectic manifolds. 268
19 1 The generalized Taylor homomorphism 268
19.2 Deformations of the algebra CH(x0,C) 270
19 3 Formal deformations of the algebra C°°(V,C) 272
19.4 Formal deformations of the algebra C°°{V,R) 273
19.5 The Moyal product 274
19.6 Selected references 275
x CONTENTS
Appendices :
20 The primitive idempotents of the Clifford algebras and the amor
phic spinor fiber bundles. 276
20.1 Preliminaries [1, d] 276
20.2 Amorphic spinoriality groups 277
20.3 Idempotents and anti involutions 278
20.4 Examples and comments 281
20.5 Amorphic spinor bundles 288
20.6 Epilogue 294
20.7 Complements 295
20.8 Selected references 298
21 Self dual Yang Mills fields and the Penrose transform in the spinor
context. 299
21.1 Introduction and basic notions 299
21.2 The Penrose transform as a resurgence of Cartan s work 302
21.3 References 309
22 Symplectic structures, complex structures, symplectic spinors and
the Fourier transform. 311
22.1 Introduction 311
22.2 Elementary notions 312
22.3 Symplectic recalls 313
22.4 Some algebraic results 315
22.5 The Fourier transform and the complex structure J 317
22.6 Bilinearity and sesquilinearity. The symplectic spin Parseval Plan
cherel theorem 322
22.7 The laplacian and the symplectic geometry 325
22.8 Some other applications 328
22.9 Selected references 330
23 Bibliography. 332
23.1 Clifford algebras and orthogonal spinors 332
23.2 Symplectic algebras and symplectic spinors 339
Notation index. 341
Subject index. 344
|
| any_adam_object | 1 |
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| id | DE-604.BV002642166 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:47Z |
| institution | BVB |
| isbn | 0792305418 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001695333 |
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| owner_facet | DE-12 DE-384 DE-91 DE-BY-TUM DE-739 DE-29T DE-19 DE-BY-UBM DE-706 DE-11 DE-188 |
| physical | XIII, 350 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Crumeyrolle, Albert 1919-1992 Verfasser (DE-588)119356104 aut Orthogonal and symplectic Clifford algebras spinor structures by Albert Crumeyrolle Dordrecht [u.a.] Kluwer 1990 XIII, 350 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 57 Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf Clifford-Algebra (DE-588)4199958-7 s DE-604 Mathematics and its applications 57 (DE-604)BV008163334 57 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001695333&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crumeyrolle, Albert 1919-1992 Orthogonal and symplectic Clifford algebras spinor structures Mathematics and its applications Clifford-Algebra (DE-588)4199958-7 gnd |
| subject_GND | (DE-588)4199958-7 |
| title | Orthogonal and symplectic Clifford algebras spinor structures |
| title_auth | Orthogonal and symplectic Clifford algebras spinor structures |
| title_exact_search | Orthogonal and symplectic Clifford algebras spinor structures |
| title_full | Orthogonal and symplectic Clifford algebras spinor structures by Albert Crumeyrolle |
| title_fullStr | Orthogonal and symplectic Clifford algebras spinor structures by Albert Crumeyrolle |
| title_full_unstemmed | Orthogonal and symplectic Clifford algebras spinor structures by Albert Crumeyrolle |
| title_short | Orthogonal and symplectic Clifford algebras |
| title_sort | orthogonal and symplectic clifford algebras spinor structures |
| title_sub | spinor structures |
| topic | Clifford-Algebra (DE-588)4199958-7 gnd |
| topic_facet | Clifford-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001695333&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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