|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Naber G.L. — The geometry of Minkowski spacetime: an introduction to the mathematics of the special theory of relativity |
|
|
|
| Предметный указатель |
 -emission 94
2-form 130
3-vector 22
3-vector, direction 23 90
3-vector, relative momentum 88
3-vector, velocity 22
4-acceleration 56
4-momentum of a material particle 88
4-momentum of a photon 90
4-tensors 144 149
4-vector, contravariant 150
4-vector, covariant 150
4-velocity 56
Aberration formula 93
Accelerations 41 58 60
Active transformation 79
Addition of velocities formula 28
Admissible basis 20
Admissible frame of reference 3 20
Admissible frame of reference, nonexistence of 6
Anti-isomorphism 167
Barn paradox 45
Bilinear form 7
Bilinear form, components of 129
Bilinear form, matrix of 128
Bilinear form, nondegenerate 7
Bilinear form, skew-symmetric 160 161
Bilinear form, spinor equivalent of 203
Bilinear form, symmetric 7
Binding energy 95 97
Binomial expansion 88
Biot — Savart law 136
Bivector 129 188
Bivector, spinor equivalent of 189
Boost 28
Canonical basis 114 117
Canonical forms 113 115 117
Carriers of a representation 146 147
Cartan, E. 143
Catenary 125
Causal automorphism 4 65 224 225
Causal precedence 64
Causality assumption 4
Causality relations 64
Cayley — Hamilton theorem 111
Change of basis formula 144
Characteristic equation 106
Charge 100
Charge-to-mass ratio 125
Charged particle 100
Chronological precedence 64 223
Clock Hypothesis 52
clocks 2 25
Clocks, atomic 2
Clocks, synchronization of 2 3
Commutation relations 178
Compton effect 95
Compton wavelength 97
Cone 4 17
Cone, null 11
Cone, time 17
Configuration space 235
Conjugate isomorphism 167
Conjugate spin covector 167
Conjugate spin vector 167
Conjugate spinor 177
Conjugate transpose 75
Conjugation representation 154
Connectible by a light ray 11
Conservation laws 87
Conservation of energy 94
Conservation of momentum 94
Conservation of world momentum 94
Constant electromagnetic fields 12 133
Constant loop 231
Contact interaction 93
Contraction 175
Contravariant rank 148—150 169
Contravariant vectors 150
Coordinate transformation 4
Coordinates, spatial 1 10
Coordinates, time 10
Cosmic rays 24
Coulomb field 133
Coulomb field, total energy of 135
Covariant rank 148—150 169
Covariant vectors 150
Covectors 147 150
Covering map 233
Covering transformation 233
Curve 51
Curve, component functions of 51
Curve, E-continuous future- (past-) timelike 211
Curve, null 52
Curve, reparametrization of 52
Curve, smooth 51
Curve, spacelike 52
Curve, timelike 52
Decay 94
Dilation 66
Dilation time 24 39
Dirac 143 144
Dirac equation 143
Dirac, Scissors Problem 227
Direct sum 47
Direction 3-vector of a photon 90
Direction 3-vector of a reference frame 23
Disintegration 94
Displacement vector 11
Displacement vector, null 11
Displacement vector, spacelike 61
Displacement vector, timelike 46
Distance 62
Distance, measured with clocks 62
Divergence 127
Dominant energy condition 121 132 205
Doppler effect 91
Doppler effect, transverse 92
Double cover 238
Dual basis 147
Dual of a bivector 131
Duration 47
E-continuous curve 211
E-continuous curve, future-timelike 212
E-continuous curve, future-timelike at  211
E-continuous curve, past-timelike 212
E-continuous curve, past-timelike at 212
E-continuous curve, timelike 212
E-continuous curve, timelike vs. smooth timelike 212
E-continuous map 211
E-distance 210
E-open ball 211
E-open set 211
E-topology 211
Eigenspace 105
Eigenspinor 200
Eigenvalue of a linear transformation 105
Eigenvalue of a spinor 200
Eigenvector 105
Einstein summation convention x-xi
Electric 3-vector 100 102
electromagnetic field 100 126 129
Electromagnetic field, constant 121
Electromagnetic field, null 107 113 201
Electromagnetic field, regular 107 113 201
Electromagnetic field, spinor 196
Electromagnetic spinor 196
Electromagnetic waves, simple, plane 136 138
Electromagnetic waves, spherical 3
Electron 143
| Electron, spin 143 227
Energy 89
Energy, Coulomb field 135
Energy, density 119
Energy, of a photon 90
Energy, total relativistic 89
Energy-momentum 88
Energy-momentum transformation 117
Energy-momentum transformation, spinor form of 203
Equation of motion 100
Euler angles 79
Events 1 9
Expansion factor 72
Extended complex plane 81
Exterior derivative 130
Feynman path 220
Feynman track of an electron 220
Field equations 208
Field of vision 86
Fizeau procedure 3
Flag pole of a spin vector 188 226
Fractional linear transformations 75 83
Frame of reference, admissible 1—6 10 20
Free charged particle 100
Free particle 93
Frequency of a photon 90
Fundamental group 231
Fundamental group, of  236
Fundamental group, of  234 235
Fundamental group, of a product 231
Future null cone 11
Future null direction 80
Future time cone 17
Future-directed, null curve 52
Future-directed, null vector 17
Future-directed, timelike curve 52
Future-directed, timelike vector 17
General linear group 145
Gravitation 1
Gravitation, negligible 6
Group of trantiformationH 15
Group representations 143 146
Hermitian matrix 75
Homeomorphism group 224
Homomorphism 78 146
Homotopic paths 230
Homotopy 230
Hyperbolic form of the special Lorent transformations 29
Hyperbolic motion 58—60
Identity representation 154
Index of an inner product 9
Inelastic collision 97
Inertial mass 88
Infeld — van der Waerden symbols 182
Initial point on a worldline 94
Inner product 7
Inner product, indefinite 7
Inner product, index of 7
Inner product, Lorentz 9
Inner product, negative definite 7
Inner product, positive definite 7
Instantaneous rest frame 58
Invariant subspace of a linear transformation 106
Invariant subspace of a representation 151
Kennedy — Thorndike 3
Kernel 104
Length 42
Length, contraction 43
Levi-Civita symbols 130
Levi-Civita symbols, spinor equivalent of 207
Light cone 11
Light cone, future and past 17
Light ray 11
Light ray, as an intersection of null cones 12
light signals 3
Light travel time 3
Lightlike vector 10
Loop 230
Loop, constant (trivial) 231
Lorentz contraction 43
Lorentz contraction, invisibility of 85
Lorentz group 15 21
Lorentz group, general homogeneous 21
Lorentz group, inhomogeneous 21
Lorentz group, two-valued representations of 152
Lorentz inner product 9
Lorentz inner product, spinor equivalent of 203
Lorentz invariant 144 150
Lorentz transformations 5 14
Lorentz transformations, boost 28
Lorentz transformations, decomposition of 30
Lorentz transformations, determined by three past null directions 85
Lorentz transformations, effect on past null directions 84
Lorentz transformations, general homogeneous 14
Lorentz transformations, hyperbolic form 29 30
Lorentz transformations, improper 20
Lorentz transformations, invariant null directions of 85
Lorentz transformations, nonorthochronous 16
Lorentz transformations, orthochronous 5 16
Lorentz transformations, proper 20
Lorentz transformations, special 27
Lorentz transformations, vs fractional linear transformations 74—84
Lorentz World Force Law 100
Lowering indices 172 176
Magnetic 3-vector 100 102
Mass, inertial 88
Mass, proper 88
Mass, relativistic 88
Mass-energy equivalence 89
Material particle 87
Material particle, free 88
Material particle, worldline of 52
Matrix group 145
Matrix group, order of 145
Matrix group, representation of 146
Matrix of a bilinear form 128
Maxwell's equations 101 127 129 131
Maxwell's equations, solutions of 133—142
Maxwell's equations, spinor form of 208
Measuring rods 43 44
Metric 210
Metric, equivalent 211
Michelson — Morley 3
Minkowski diagram 34
Minkowski spacetime 9
Multilinear functional 149
Neutrino equation 208
Null basis 10
Null cone 11
Null cone, future 18
Null cone, past 18
Null direction 80
Null direction, future 80
Null direction, past 80
Null electromagnetic field 201
Null flag 194 226
Null vector 10
Null vector, future-directed 18
Null vector, orthogonal 10
Null vector, parallel 10
Null vector, past-directed 18
Null worldline 11
Observer 1
Observer, admissible 1 20
Open set in  126
Orientation-entanglement relation 237
Orthochronous 5 16 66 225
Orthogonal complement 7
Orthogonal transformations 12
Orthogonal transformations, and causal automorphisms 66
|
|
|
| Реклама |
|
|
|
|
|
О проекте