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Schutz B. — Geometrical Methods in Mathematical Physics
Schutz B. — Geometrical Methods in Mathematical Physics

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Название: Geometrical Methods in Mathematical Physics

Автор: Schutz B.

Аннотация:

This book is only readable AFTER you have read Schutz "Introduction to general relativity", the latter is a much better book.One key flaw is that the author tries to cover lots of stuff in very little space, which requires read to take leap of faith. Lie group and Lie algebra are not covered well in this book."Tensor Analysis on Manifold" is a good alternative on differential geometry, but the fonts are too small.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 1980

Количество страниц: 260

Добавлена в каталог: 12.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$R^{n}$      1
Accelerated observer      71
Adiabatic      182 183
Adjoint transformation      107
Affine connection      76 201—222 218 221
Affine connection, linearity      204 Affine connection metric
Affine connection, torsion      207
Affine parameter      209 218
Analytic function      9 10
Analytic manifold      26
Angular momentum operators      85 Angular momentum operators as Killing vector fields
Annihilate      154
Annulling a form      120 153 166
Antiderivation      134
Antisymmetric tensor      115
Area      113 Area tensor
Atlas      25
Automorphism      107
Axial eigenvalue      90 91
Axial harmonics, scalar      90 Axial harmonics vector
Axial symmetry      87 89 Axial
Axial vector      126
Basis      14 Basis Cartesian
Basis transformation      60 Basis transformation matrix
Basis, dual      55 Basis for one-forms
Basis, transformation of      60
Basis-invariance      63
Betti number      152
Bianchi identities      212
big bang      199
Bijection      7
Boundary of a region      144
Canonical energy      173
Canonical momentum      173 221
Canonical transformation      168
Caratheodory's theorem      165
Cartan, E.      113
Chart      24
Christoffel symbols      205 218 Christoffel
Closed form      138 Closed form locally
Closed form on a sphere      150 Closed form sufficient
Closed ideal      163
Closed set of forms      158
Cofactor      18
Cohomology      139 142 150 Cohomology
Commutator      44 Commutator of covariant derivatives
Compatibility of connection and differential structure      204 Compatibility of connection and metric
components      see "Individual types of tensor"
Composition of two maps      7
Configuration space      174
Congruence      43 151
Connection one-form      220
Connection, metric      216
Conservation law      89 149 158 163 171 173 182
Conservative      168
Conserved quantities and Killing vector fields      171
Continuity, function      7 8 Continuity group
Continuity, one-form      52 Continuity space
Continuum mechanics      58
Contraction      50 56 59 Contraction
Coordinate transformation      31 62 255
coordinates      23 24 Coordinates curvilinear
Copernican Principle      189
Cosmological principle      18 9
Cosmology      161 136—199 Cosmology big
Cosmology, closed      198 199 Cosmology expanding
Cosmology, isotropic      187 189 Cosmology open
Cosmology, standard model      199
Cotangent bundle      53 174 175
Covariant derivative      184 203 Covariant commutator
Covariant derivative, Jacobi identity for      212 Covariant derivative Leibniz
Cross-product      125 126 Cross-product triple
Cross-section      38 53 220
Curl      136 176
Curvature      68 214
Curve      30 153 Curve congruence
Curve, geodesic      208 Curve parameter
Density, scalar      129 Density tensor
Diffeomorphism      30 73 92 188
Differentiability class of a function      8 Differentiability class of a one-form
Differential form      68 117 Differential annulling
Differential form, field      120 Differential form independent
Differential form, sectioning      120
Differential forms, annihilate of      154
Differential forms, closed ideal      163 Differential forms closed
Dirac bra and ket      51
Dirac delta function      51
Direct product      59
Directional derivation      33 53
Directional derivative      33 53
Discrete set      2
Distance function      1 3—5
Distance on a manifold      68 70
Distribution (of vector fields)      83
Distribution (over functions)      51
Divergence      137 176 196 Divergence
Divergence theorem      147
Domain of an operator      11
Dual      186 196 Dual double
Duality of vectors and one-forms      50
Eigenvalue      19 65 96 99
Eigenvector      19
Einstein summation convention      56 62
Electromagnetism      175—181 Electromagnetism as a gauge theory
Electromagnetism, one-form potential      180 221 219
Electromagnetism, plane waves      181 Electromagnetism polarization
Electromagnetism, vector potential      180
entropy      163 166 167 182 183
Equation of continuity      149
Equation of state      163
Equivalence class      150
Equivalence relation      150
Ertel's theorem      185
Euclidean space      15 65 79 121 161 176 182 197 198 214 218
Euclidean vector algebra      68 125 131 132
Euclidean vector calculus      70 136 137 142 147 148 182
Exact form      138 163 170 Exact
expansion      186
Exponential map      167 210 215
Exponentiation of an operator      43 Exponentiation of covariant derivative
Exterior derivative      134 Exterior derivative commutes
Faraday tensor      176 221
Fiber bundle      35 36 40 53 183 220 Fiber base
Fiber bundle, fiber      36 40 Fiber global
Fiber bundle, globally trivial      38 Fiber bundle locally
Fiber bundle, structure group      40
Fixed-point theorem      39 151 196
Flat manifold      172 214
Fluid dynamics      149
Fluid, multicomponent      164 Fluid perfect
Fluid, single-component      163
Foliation      81 108 188 Foliation leaf
Frame bundle      42
Frobenius' Theorem      81 82 153—155 163 165 166
Function      5 30
Function space      51
Function, analytic      9 10 Function
Fundamental theorem of calculus      134
Galilean spacetime      182 183 218
Gauge curvature two-form      221 Gauge theories
Gauge-covariant derivative      220
Gauss' theorem      147 148
Geodesic curve      208 Geodesic curve affine
Geodesic deviation      213 214
Geodesic equation      208
Geodesically complete manifold      210
Geometrical object      62
Gl(n, c)      100
GL(n, R)      41 95 GL(n R) acting
Gradient      53 Gradient not
Grassmann algebra      118 125
Group      11—13 Group abstract
Group, rotation      29 98 99 Group translation
Hamiltonian, equations      167 Hamiltonian equations function
handedness      see "Basis"
harmonic oscillator      153 159
Hausdorff property      3
Helmholtz circulation theorem      185
Hermitian conjugate      100
Hilbert space      51 108
Homeomorphism      40
Homogeneous      187 188 191
Homomorphism      102 104
Hypersurface      79 167 178 182 183 188 see
Ideal, closed      163 Ideal complete
Identity transformation      17
Image      6
Index notation      73
Index raising and lowering      68
Indices, antisymmetrized      166 Indices placement
Infinitely differentiable      9
Inner automorphism      107
Inner product      15 51 71
Integrability conditions      138 155
Integration      134 Integration and orientation
Integration of functions      121
Integration, change of variables      9 Integration of forms
Into (map)      7
Invariance of a tensor field      86 see
Inverse function theorem      9 35 49
Inverse image      6
Inverse map      6
inversion      99
Isometry      188 190
Isospin      37
Isotropic      187 189
Jacobi identity for covariant derivatives      212 Jacobi identity for Lie derivatives
Jacobian      9 122 129 132
Jacobian matrix      9 35 63
Killing vector field      88 108 171 188 192 195 216 Killing nonexistence
Killing's equation      216
Klein — Gordon equation      174 219
Kronecker delta      17
Lagrangian function      167 174
Left-invariant vector field      93—95
Leibniz rule for covariant derivative      204
Leibniz rule for exterior derivative      134 Leibniz rule for Lie derivative
Levi-Civita symbol      128 Levi-Civita symbol and determinants
Lie algebra      47 92 93 95 97 101 155 170 Lie Abelian
Lie algebra of invariant vector fields      87 Lie algebra of isometry group
Lie bracket      45 75 157 Lie closure
Lie derivative      68 173 182 184 Lie
Lie derivative of a scalar      76 Lie derivative of a tensor
Lie dragging      73 90 209 213 Lie
Lie group      12 29 87 92 188 Lie abelian
Lie group, adjoint representation      189 Lie group and invariance
Lie subalgebra      192
linear combination      14
Linear independence      14
Linear transformation      16 Linear transformation components
Liouville's theorem      171
Lorentz frame      70 71
Lorentz group      67 192
Lorentz transformation      67 219
Manifold      23 Manifold analytic
Manifold, isotropic      189 Manifold maximally
Manifold, Riemannian      169 201—222 Manifold simply
Many-to-one      6
MAP      5 Map composition
Map, generated by a congruence      73 Map into
Map, inverse      6 Map many-to-one
Map, stereographic      27
Matrix      50 Matrix anti-Hermitian
Matrix, nonsingular      17 Matrix orthogonal
Maxwell identities      164 169
Maxwell's equations      175—181
Metric      36 38 51 54 76 113 169 178 184 201 215 Metric Euclidean
Metric connection      216
Metric dual      128 133
Metric tensor      64 187 214 Metric
Metric tensor field      68 108 Metric local
Metric volume element      132 148 160 193
Metric, Minkowski      66 71 Metric signature
Minkowski metric      66
Minkowski space      70 79 179 214 217 218 219 220
Moebius band      39 Moebius band not
Moebius band, structure group      42
Multilinearity      57
n-tuple      1 15 23
n-vector      125
Neighborhood      1 Neighborhood generalized
Newtonian gravity      187
Norm      14 Norm Euclidean
Normal coordinates      210
Normal one-form      147
O(N)      66 98 O(n)
O(n), dimension of      99
One-form      49 One-form as a tensor
One-form, components      55 One-form coordinate
One-form, dual basis      55 One-form field
One-form, picture of      53
One-parameter subgroup      94 95 One-parameter infinitesimal
One-to-one      6
Onto (map)      7
Open set in $R^{n}$      2 3
Operator      10 Operator as a tensor
Operator, extension of      11 Operator multiplicative
Orientability      41 132 175 Orientability internal
Orientation, external      123 Orientation internal
Orthogonal group      see "O(n)"
Outer product      59 64
p-delta symbol      130 p-delta symbol contraction
Parallel transport      202 204 Parallel
Parallelism      76 201 Parallelism global
Parallelogram rule      15
Partial differential equations      134 137 152 Partial integrability
Permutation group      12
Phase space      28 168 174 Phase volume
Poincare lemma      140
Poisson bracket      170
Principle of equivalence      218
Principle of mediocrity      189
Principle of minimal coupling      218
Product space      38
Proper distance and time      70
Pseudo-norm      15 71
quantum mechanics      51 Quantum mechanics commutation
Quotient space      150
R      2
Realization      106 Realization faithful
Relativity      38 188 Relativity general
Relativity, special      66 68 70 219
Representation      106 Representation abstract
Restriction of a form      120 153 188
Ricci scalar      217
Ricci tensor      217
Riemann tensor      211 213 Riemann number
Riemannian geometry      76 184 187
Riemannian manifold      169 201—222
Right-invariant vector field      94
Rotation group      see "SO(3)"
Rule of linearity      16
scalar      64 Scalar covariant
Sectioning a form      120
Shear      186
Signature      66 68 69
Similarity transformation      19 65
Simply connected manifold      102 Simply connected manifold and cohomology
SO(2)      92
SO(3)      29 98 99 100 111 160 190 192;
1 2
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