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O'Donnel P. — Introduction to 2-Spinors in General Relativity
O'Donnel P. — Introduction to 2-Spinors in General Relativity

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Название: Introduction to 2-Spinors in General Relativity

Автор: O'Donnel P.

Аннотация:

O'Donnell (Anglia Polytechnic University, UK) introduces 2-spinor formalism in general relativity in this text for those at the graduate and research levels. The text begins by developing spinors in a geometrical way, then concentrates on the algebra and calculus of spinors connected with curved space-time. The text concludes with an analysis of the Lanczos spinor. Exercises are included


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 204

Добавлена в каталог: 10.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$SL(2, \mathbb{C})$      8 24 64
Abstract index notation      11 14—16
Affine connexion      92 152
Affine Minkowski space      127
Affine parameter      160
Algebraically general      34 36 87
Algebraically special      34 36 87 118
angular momentum      171
Angular momentum vector      141
Angular velocity vector      141
Anti-celestial sphere      6
Anti-self-dual      32
Antipodal transformation      12
Asterisk operation      73
Bampi, F.      99
Basis      17
Basis, complex null      52
Basis, dual      17 52
Basis, natural      129 131 133
Basis, orthonormal      3 105 146
Basis, spinors      20
Basis, vectors      1
Bianchi identities      50 87 92 158
Bianchi identities, contracted      51 158
Bianchi identities, GHP form      85
Bianchi identities, spin coefficient form      62
Bianchi identities, spinor equivalent      51
Bivalent spinor      16 23
Bivector      31
Bondi, H.      75
Boost      see “Lorentz boost”
Boost parameter      68 76
Boost-weight      81
Canonical decomposition of symmetric spinors      33 34
Canonical decomposition of the Weyl spinor      36
Carmeli, M.      1
Cartan, E.      1
Caviglia, G.      99
Celestial sphere      5
Chart      128 130 131 133
Christoffel symbols      49 92 148 152
Classical mechanics      140
Commutation relations      58 119
Complex conjugate, spinor basis elements      22
Complex conjugation of spinor components      15
Complex field      10
Complex null basis      52
Complex plane      6
Complex plane, extended      6
Conformal transformation      7
Conjugated weighted differential operators      82
Connexion coefficients      148
Conservation of energy      145
Conservation of linear momentum      145
Conservation of mass      145
Contracted Bianchi identities      51
Contracted Bianchi identities, GHP form      85
Contraction      15 136
Contravariant vector field      158
Contravariant vectors      132
Coordinate neighbourhood      128
Coordinate transformation      131
Cosmological constant      45
Cosmological term      163
Covariant derivative      151
Covariant derivative, axioms      152
Covariant derivative, properties      39
Covariant derivative, spinor      39
Covariant vectors      132
Curvature scalar      see “Ricci scalar”
Curvature spinors      42 47 49 59
Curvature tensor      see “Riemann tensor”
Cvitanovic, P.      14
Cyclic condition      101
Deflexion of light      173 174
Dirac, equation for the electron      93
Dirac, Scissors Problem      12
Directional derivatives      see “Intrinsic derivatives”
directions      5
Directions, future-pointing, null      5 76
Directions, future-pointing, timelike      5
Directions, past-pointing, null      5
Directions, past-pointing, timelike      5
Directions, principal null      31 33—36 87 118
Directions, spacelike      6
Directions, timelike      6
Divergence      146
Dual anti-self-      32
Dual basis      17 132
Dual space      15 132
Dual tangent space      132
Dual, basis      52
Dual, left-      32
Dual, self-      32
Dummy indices      17 131
Dyad      20
Dyad, components      52
Edgar, S.B.      99
Einstein field equations      45 75 92 163 166
Einstein field equations, spinor equivalent      45
Einstein summation convention      1 135
Einstein tensor      52 94 158 162 163
Einstein tensor, spinor equivalent      45
Einstein — Cartan — Sciama — Kibble theory      40
Einstein, A.      75 91 92
Electromagnetic field tensor      31 35
Electromagnetic spinor      32 33
Electromagnetic spinor, classification of      34
Empty space field equations      45
Energy-momentum tensor      45 92 146 162
Epsilon spinor      see “Levi — Civita spinor”
Equation of continuity      145
Euclidean space      6 128 130
Euler — Lagrange equations      161 170
Euler’s equation      145
Event in space-time      127 128
Field, gravitational      162
Field, scalar      142
Field, scalar, gradient      143
Field, spinor      80
Field, tensor      80 142
Field, tensor, components      142
Field, vector      142
Flag plane      8—10
Flagpole      8 10
Geodesic      161
Geodesic coordinate system      148
Geodesic equation      159
Geodesic, null      163
Geodesic, timelike      163 165 170
Geroch — Held — Penrose formalism      see “GHP formalism”
Geroch, R.      76
GHP field equations      82
GHP formalism      75 77
Goldberg — Sachs theorem      118
Goldberg, J.N.      87
Gravitational field      162
Gravitational field, static      164 168
Gravitational radiation problem      75
Gravitational red shift      175 176
Gravitational spinor      see “Weyl spinor”
Gravitational waves      75
Held, A.      76 86
Hermitian matrix      24
Holomorphic transformation      7
Homomorphism, $SL(2, \mathbb{C})$ and L(4)      24
Huggett, S.A.      12
Hulse — Taylor binary pulsar      75
Hulse, R.A.      75
Hyperplane      5 6
Illge, R.      99
Indices, contravariant      15 134
Indices, covariant      15 134
Indices, dummy      17
Indices, numerical      1 17 49
Indices, tetrad      62
Infeld-van der Waerden symbols      24—26
Inner product      2 15 136
Intrinsic derivatives      56 80 117
Jacobian      127 132
Kasner, E.      124
Kennedy, A.D.      14
Kinnersley null tetrad      117
Kinnersley, W.      117
Kronecker delta      see “Kronecker symbol”
Kronecker spinor      53
Kronecker symbol      19 20 26 136
L(4)      24 64
Lagrange multipliers      92 93
Lagrange multipliers, trace      93
Lagrange multipliers, trace-free      93
Lagrangian      92—94
Lagrangian, tensor, local      99
Lanczos      96
Lanczos coefficients      105 114—117 119
Lanczos coefficients, $l\leftrightarrow n$ and $m \leftrightarrow -\bar{m}$      112
Lanczos coefficients, asterisk operation      113
Lanczos coefficients, null rotations      110
Lanczos coefficients, prime operation      113
Lanczos coefficients, spin boost transformation      111
Lanczos potential      see “Lanczos tensor”
Lanczos spinor      99 101
Lanczos spinor, symmetry properties      102
Lanczos tensor      93 96 97 99
Lanczos tensor, spinor equivalent      100
Lanczos, C.      91 120
Lanczos, canonical variables      93
Lanczos, coefficients      104
Lanczos, cyclic condition      93
Lanczos, divergence-free      97 103
Lanczos, gauge conditions      97 101
Lanczos, trace-free      97
Left-dual      32
Levi — Civita spinor      11 16 18 19 23 32
Levi — Civita tensor      32
Liebniz’s law      40
Linearity      10
Lorentz boost      64 67 109 117
Lorentz group      64 76
Lorentz transformations      64
Lorentz, factor      144
Lorentz, group      24
Lorentz, scalar product      146
Lorentz, transformations      3
Lorentz, transformations, active      3 4
Lorentz, transformations, passive      3
Lorentz, transformations, restricted      3
Lorentzian metric      1
Lorentzian signature      150 161
Maher, W.F.      106
Malin, S.      1
Manifold, differentiate      128 146
Manifold, differentiate, four-dimensional      128 131 150
Manifold, differentiate, n-dimensional      128 131
Manifold, differentiate, one-dimensional      130
Manifold, differentiate, two-dimensional      128 130 131
Manifold, Euclidean      140
Manifold, Riemannian structure      154
Manifold, tangent space      131
Massa, E.      99
Matrix, hermitian      24
Matrix, Pauli spin      24
Matrix, spin      8
Maxwell spinor      see “Electromagnetic spinor”
Mercury, perihelion of      173
Metric tensor      92 93 95 146 159 161
Minkowski coordinates      2 3 28
Minkowski geometry      127
Minkowski space      1 20 36
Minkowski space, affine      127
Minkowski space, non-singular      2
Minkowski space, time-orientation      2 3 27
Minkowski tensor      99 146 148
Minkowski tetrads      2 3
Minkowski tetrads, improper      3
Minkowski tetrads, orthochronous      2 3
Minkowski tetrads, proper      3
Minkowski tetrads, restricted      3
Misner, C.W.      12
Modified GHP formalism      86
Modified GHP operators      86
Moment of inertia tensor      142
Multivalent spinors      15
Natural basis      133
Natural basis vectors      129 131
Newman — Penrose field equations      see “NP field equations”
Newman — Penrose spin coefficient, formalism      see “NP formalism”
Newman, E.      52
Newtonian theory      164
Newton’s gravitational constant      see “Universal gravitational constant”
Non-normalised spin basis      54
Novello, M.      115
NP field equations      59 60
NP formalism      52
Null cone      5—8
Null curve      160
Null directions      35
Null flag      8 9 13
Null geodesic      163
Null geodesies, shear-free      87
Null rays      5
Null rotations, Lanczos coefficients      110
Null rotations, spin coefficients      65
Null rotations, with 1 fixed      65
Null rotations, with 1 fixed, curvature spinor components      65
Null rotations, with 1 fixed, spin basis      65
Null rotations, with 1 fixed, Weyl spinor components      66
Null rotations, with n fixed, curvature spinor components      67
Null rotations, with n fixed, spin basis      66
Null rotations, with n fixed, spin coefficients      66
Null rotations, with n fixed, Weyl spinor components      67
Null tetrad      27 29 77 104
Null vectors      2 5 28
Orbiting planet      170
Orientation      3
Orthochronous Lorentz group      64
Orthonormal      146
Orthonormal basis      105
Orthonormal tetrad      28 29
Orthonormalisation conditions      20 28 29
O’Donnell, P.      117
Pagani, E.      99
Particle, four velocity      142 165
Particle, world line      142
Pauli spin matrices      24
Payne, W.T.      10
Penrose, R.      11 12 14 52 76
Petrov classification      34 35
Petrov type      36
Petrov type, algebraically general      36
Petrov type, algebraically special      36
Petrov type, degenerate      36
Petrov type, null      36
Poisson’s equation      162 166
Preferred parameter      160
Prime operation      71 77
Principal null directions      31 33—36 87 118
Principal spinors      34 36
Principle of covariance      150
Principle of equivalence      149 150 162
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