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Lounesto P. — Clifford algebras and spinors
Lounesto P. — Clifford algebras and spinors

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Название: Clifford algebras and spinors

Автор: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2001

Количество страниц: 346

Добавлена в каталог: 08.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$KS$- transformation      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$\ddot{o}$dinger      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 $= KS$      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$\ddot{o}$dinger equation      50
Schr$\ddot{o}$dinger — 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 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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