Naber G.L. — The geometry of Minkowski spacetime: an introduction to the mathematics of the special theory of relativity :: Электронная библиотека попечительского совета мехмата МГУ

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Naber G.L. — The geometry of Minkowski spacetime: an introduction to the mathematics of the special theory of relativity

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Название: The geometry of Minkowski spacetime: an introduction to the mathematics of the special theory of relativity

Автор: Naber G.L.

Аннотация:

It is the intention of this monograph to provide an introduction to the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. Particular care has been exercised in keeping clear the distinction between a physical phenomenon and the mathematical model which purports to describe that phenomenon so that, at any given point, it should be clear whether we are doing mathematics or appealing to physical arguments to interpret the mathematics.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 259

Добавлена в каталог: 19.07.2005

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Предметный указатель

Orthogonal transformations, and fractional linear transformations      74—87
Orthogonal transformations, and homeomorphisms      225
Orthogonal transformations, associated matrices      13
Orthogonal transformations, invariant null directions      85
Orthogonal transformations, orthochronous      66
Orthogonality      7
Orthogonality of null vectors      10
Orthogonality of spacelike and null vectors      63
Orthogonality of spacelike vectors      63
Orthogonality with timelike vectors      16
Orthonormal basis      8
Outer product      175
P-continuous curve      219
P-continuous curve, characterized as Feynman paths      220
P-continuous curve, vs E-continuous curves      219
P-continuous curve, vs timelike curves      219
P-open set      215
P-open set, not E-open      216
Paradox, barn      45
Paradox, twin      40 60
Parity nonconservation      209
Particle, charged      100
Particle, free      93
Particle, free charged      100
Particle, material      87
Passive transformation      79
Past null cone      17
Past null direction,      80
Past time cone      17
Past-directed, null curve      52
Past-directed, null vector      17
Past-directed, timelike curve      52
Past-directed, timelike vector      17
Path      230
Path connected      221 230
Path topology      215
Path topology, base for      216
Path topology, homeomorphisms of      224 225
Path topology, topological properties of      218 219 221
Path, inverse of      230
Path, products      230
Pauli spin matrices      75 178
Phase factor      191
Photon      1 90
Photon, direction 3-vector of      90
Photon, energy      90
Photon, frequency      90
Photon, propagation of      3
Photon, wavelength      91
Photon, world momentum of      90
Photon, worldline      90
Pions      39
Planck's constant      91
Poincare group      21
Point event      1
Poynting 3-vector      119
Principal null directions      115 117 121 198 206
Product path      230
Proper mass      88
Proper spatial separation      61
Proper time function (parameter)      55
Proper time length      52
Proper time separation      48
Pythagorean Theorem      63
Quadratic form      7
quantum mechanics      143 150 208 209
Raising indices      172 176
RANGE      104
Rank, contravariant      148—150 169
Rank, covariant      148—150 169
Real projective n-space      234 235
Real projective n-space, fundamental group of      234 23
Region in $\mathcal M$       126
Regular electromagnetic field      201
Relative 3-momentum      88
Relativistic electron      143 238 239
Relativistic energy      89
Relativistic mass      88
Relativity of      25 34—38
Relativity of simultaneity      25 34—38
Relativity principle      6
Representations      143 146 147
Representations, carriers of      146 147
Representations, equivalent      151
Representations, irreducible      151 169
Representations, reducible      151 169
Representations, spinor      153
Representations, two-valued      150 152
Reversed Schwartz inequality      48
Reversed triangle inequality      49 50
Riemann sphere      79—81
Rigidity      43
Robb's Theorem      62
Rocket twin      51 60
Rotation group      236
Rotation in $\mathcal L$       22
Rotation subgroup of $\mathcal L$       22
Schur's lemma      151
Schwartz Inequality for $\mathbb R^3$       10
Schwartz Inequality, reversed      48
Signals      3
Simply connected      231
Simultaneity      25
Simultaneous      6 25 34—38
Skew-symmetric      177 178
Skew-symmetric bilinear form      128
Skew-symmetric linear transformation      101
Skew-symmetric linear transformation, null      107 201
Skew-symmetric linear transformation, regular      107 201
Skew-symmetrization      178
Smooth assignment      126
Smooth real-valued function      126
Smooth vector field      127

Spacelike displacement      61
Spacelike vector      12
Spatial coordinates      1
Special linear group      75
Special Lorentz transformation      27
Special Lorentz transformation, hyperbolic form of      29
speed of light      3
Speed of material particles      29
Spin      143 208
Spin covector      164
Spin frame      161 162
Spin space      161
Spin transformation      75
Spin vector      161
Spinor      143 152 160 161 168
Spinor equivalent of a bilinear form      202
Spinor equivalent of a bivector      189
Spinor equivalent of a covector      185
Spinor equivalent of a vector      180
Spinor equivalent of a world tensor      207
Spinor equivalent of differential operators      207
Spinor equivalent of Levi—Civita symbols      207
Spinor equivalent of the dual of a bivector      207
Spinor equivalent of the Lorentz inner product      203
Spinor map      75 77 151 238 239
Spinor representations      153
Spinor representations, type of      153
Spinor, components of      168 174
Spinor, conjugate      177
Spinor, contravariant indices of      169
Spinor, covariant indices of      169
Spinor, dotted indices of      168
Spinor, electromagnetic      196
Spinor, equivalents      See spinor equivalent
Spinor, essential two-valuedness of      19 226 227
Spinor, form of Maxwell's equations      208
Spinor, Hermitian      177
Spinor, lower indices of      168
Spinor, symmetric      177 178
Spinor, undotted indices of      168
Spinor, upper indices of      168
Spinor, valence of      168
Spinor-covector      181
Spinorial object      150 226 239
Standard configuration      27
Stress tensor      119
Subgroup      146
Subgroup of C      28
Subgroup of transformations      21
Summation convention      x-xi
Symmetric linear transformation      118
Symmetrization      178
Synchronization      2 3
Synchronization, lack of      40
Temporal order      4 18 61
Tensor product      148—149
Tensorial objects      237
Terminal point on a worldline      94
Time axis      47
Time cone      17
Time coordinates      10
Time dilation      24 39
Time in units of distance      3
Time orientation      17 18
Timelike curve, E-continuous      212
Timelike curve, smooth      52
Timelike straight line      47
Timelike vector      12
Timelike vector, future-directed      17
Timelike vector, past-directed      17
Timelike worldline      52
Topological manifold      230
Topological manifold, products of      231
Topology, Euclidean (or E-)      211 212
Topology, fine      211
Topology, path (or P-)      215
Total relativistic energy      89
Total world momentum      93
Trace      118
Trace free      118
Transformation equations      4 5
Transformation matrix      145
Translation      5 66
Translation of a light ray      67
Translation of a light ray, lifts of      68
Twin paradox      40 60
Uniformly moving charge      135
Unit vector      8
Unitary matrix      78
Universal covering manifold      233
Vector field      127
Vector field, components of      127
Vector field, smooth      127
Velocity 3-vector      22
Velocity parameter      29
Velocity vector      51
Version      237
Wave equation      141
Wave function      150 227 239
Wavelength of a photon      91
Weak interactions      209
Weyl      1
Weyl, neutrino equation      208
World acceleration      56
World momentum of a material particle      88
World momentum of a photon      90
World tensors      144 148—150 160
World vectors      178
World velocity      56
Worldline      1
Worldline of a material particle      52
Worldline of a photon      90
Zeeman's Theorem      4 20 65 66 74 224 225

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