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Lounesto P. — Clifford algebras and spinors
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Название: Clifford algebras and spinorsАвтор: Lounesto P. Аннотация: This second edition of a popular and unique introduction to Clifford algebras and spinors has three new chapters. The beginning chapters cover the basics: vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters, which will also interest physicists, include treatments of the quantum mechanics of the electron, electromagnetism and special relativity. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing among the Weyl, Majorana and Dirac spinors. Scalar products of spinors are categorized by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy's integral formula is generalized to higher dimensions.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-nd editionГод издания: 2001Количество страниц: 346Добавлена в каталог: 08.12.2013Операции: Положить на полку |
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148 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 Bilinear covariants 137 142 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 dual 39 Clifford product 9 41 189 Clifford-conjugate 29 56 86 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 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 projection operator 138 Energy, kinetic 50 Energy, total 50 Equation, Dirac 136 Equation, Maxwell 101 Equation, Schr 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 Kustaanheimo — Stiefel 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 Multivector 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 metric 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, Clifford 9 Product, cross 37 Product, exterior 10 34 Product, graded tensor 202 Product, scalar 7 92 Product, scalar, of spinors 233 Quadratic form 195 Quadratic form, neutral 196 Quadratic form, space 93 195 Quadratic space 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 Schr 50 Schr 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 reversal, 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
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