Авторизация
Поиск по указателям
Lounesto P., Hitchin N.J. (Ed), Cassels J.W. (Ed) — Clifford Algebras and Spinors
Обсудите книгу на научном форуме
Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter
Название: Clifford Algebras and Spinors
Авторы: Lounesto P., Hitchin N.J. (Ed), Cassels J.W. (Ed)
Аннотация: Beginning chapters, suited for undergraduates, introduce vectors, complex numbers, and quaternions as background for material on Clifford algebras. Later chapters, also of interest physicists, treat the quantum mechanics of the electron, electromagnetism, and special relativity. Recent research on Clifford algebras is surveyed, and a new classification of spinors is introduced, based on bilinear covariants of physical observables. Scalar products of spinors are classified by involuntary anti-automorphisms of Clifford algebras. Brauer-Wall groups and Witt rings are discussed, and Cauchy's integral formula is generalized to higher dimensions. The author is affiliated with Helsinki Polytechnic Stadia.
Язык:
Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Издание: 2nd edition
Год издания: 2001
Количество страниц: 348
Добавлена в каталог: 20.05.2008
Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Algebra 21
Algebra, automorphism of 22
Algebra, Clifford 9 23 40 56 190
Algebra, division 200 301
Algebra, exterior 40
Algebra, Lie 95
Algebra, opposite 175 202
Algebra, simple 202
Alternation 194
alternative 200 301
Automorphism, similar 31
Basis 3
Basis, orthonormal 7
Basis, standard 4
Bilinear 21
Bivector 8
Bivector, opposite 34
Bivector, simple 87
Bivector, unit 25 34
Brauer group 202
Brauer — Wall group 239
Brauer — Wall — Porteous group 240
Cartan map 63
Cartan's principle of triality 308
Cayley algebra 200 303
Cayley transform 222
Cayley — Dickson process 285 302
Center 55
Charge conjugation 162 168
Clifford algebra 9 26 40 53 190
Clifford conjugate 29 56 86
Clifford product 9 41 189
Clifford, dual 39
Combination, linear 6
companion 307 317
Complex conjugate 18
Complex number 18
Conjugate, charge 162 168
Conjugate, Clifford- 29 56 86
Conjugate, complex 18
Conjugate, quaternion 69
Contraction 44 46
Coordinate 3 6
covariants 137 142
Cover(ing), two-fold 30
Crawford 152 156
Cross product 37 93
DIMENSION 6
Dimension, grading 42
Dirac adjoint 136 139
Dirac current 136
Dirac equation 135 136
Dirac matrices 135
Dirac — Hestenes equation 144
Directed line segment 1
Division algebra 200 301
Division ring 61 232
Dual, Clifford 39
Dual, Hodge 38
Endomorphism 6
Energy, kinetic 50
Energy, projection operator 138
Energy, total 50
Equation, Dirac 136
Equation, Maxwell 101
Equation, Schroedinger 50
Euclidean plane 7
Euclidean space 93
Even part 28
Exterior algebra 40
Exterior product 10 34
Field 21
Field, automorphism of 22
Field, ordering of 31
Function, linear 5
Function, right linear 73
Grade involution 29 86
Graded tensor product 202
Grading, dimension 42
Group, Brauer 202
Group, Brauer — Wall — Porteous 240
Group, Lorentz 124
Group, spin 220
Helicity 164
Hestenes 149
Hestenes, Dirac — Hestenes equation 144
Hodge dual 38
Hyperbolic plane 196
Ideal, left 52 60
Ideal, minimal 60
Idempotent 52 60
Idempotent, lattice of 227
Idempotent, primitive 52 61 138 164 226
Imaginary part 18
Inverse quaternion 70
Involution 56
Involution, grade 29 56 86
Involution, parity 169
Irreducible components 53
Irreducible fields 260
Irreducible left ideal 213
Irreducible representation 228 232
Irreducible tensor 113
Isoclinic 89 310
Isotropic 196
KS-transformation 148
Kustaanheimo — Stiefel = K S 63
Left ideal 52 60
Left ideal, graded 213
Left ideal, irreducible 213
Left ideal, minimal 52 60 226
Lie algebra 95
linear combination 6
Linear function 5
Linear isomorphism 6
Linear space 5
Linear structure 5
Linear, right 73
Linearly independent 6
Lorentz force 100
Lorentz group 124
Lorentz invariants 123
Lorentz transformation 120
Lorenz condition 106
Lorenz gauge 106
MAP see function
Mapping, see function
Matrix, Pauli spin 51 73.
Maxwell equations 101
Metric 8
Minimal left ideal 52 60 226
Minkowski space-time 102 121
Multi vector structure 43
Negative 31
Neutral axis 315
Neutral quadratic space 195
Norm 8 19 36 37 70
Null = isotropic 196
NUMBER 20
Number, complex 18
Number, negative 31
Number, positive 31
Octonion 97 303
Odd part 28
Opposite algebra 175 202
Opposite bivector 34
Opposite netric 174
Opposite product 318
Opposite vector 2
Ordering 31
Parity involution 169
Part, even 28
Part, odd 28
Pauli spin matrices 51 73
Pauli spinor 52 60
Pauli — Dirac representation 136
Polar form 19
Positive 31
Product of spinors 233
Product, Clifford 9
Product, cross 37
Product, exterior 10 34
Product, graded tensor 202
Product, scalar 7 92
Quadratic form 195
Quadratic form, neutral 196
Quadratic space 93 195
Quaternion 68
Quaternion conjugate 69
Real part 10
Real structure 139
Representation, faithful 228
Representation, irreducible 228
Representation, Pauli — Dirac 136
reversion 28 56 86
Rodrigues formula 58 71
Rotation, isoclinic 89 310
Rotation, simple 89
scalar 1
Scalar product 7 92
Scalar product of spinors 223
Schroedinger equation 50
Schroedinger — Pauli equation 64
Similar 31
Simple bivector 87
Simple Clifford algebra 228
Simple rotation 89
Space, Euclidean 93
Space, linear 5
Space, quadratic 93 195
span 6
Spin 50
Spin group 30 59 220
Spin projection operator 138
Spinor operator 63 143 145
Spinor regularization 63
Spinor representation 53
Spinor space 61
Spinor, column 138
Spinor, Dirac 164 167
Spinor, even 228
Spinor, ideal 138
Spinor, Majorana 163
Spinor, Pauli 52 60
Spinor, recovery of 155
Spinor, semi- 228
Spinor, Weyl 164
Spinoriality 169
Standard basis 4
Structure, complex 139
Structure, linear 5
Structure, multivector 43
Structure, real 139
Tensor product 197 201
Time reversal 169
Time, Wigner 169
Triality 306 309
Triality triplet 308
Triality, Cartan's principle of 308
Two-fold 30
Unit bivector 25 34
Unit circle 67
Unit vector 2
Universal 192
Vector 1 5
Vector space 4
Vector, unit 2
Witt index 196
Witt ring 198
Реклама