Szekeres P. — A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Szekeres P. — A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry

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Название: A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry

Автор: Szekeres P.

Аннотация:

Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book also includes exercises and proofed examples to test the students' understanding of the various concepts, as well as to extend the text's themes.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 600

Добавлена в каталог: 05.10.2005

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Предметный указатель

Representation irreducible      121
Representation of a group      50
Representation of a group, complex      50
Representation unitary      141
Representation, degree of      120
Residue classes modulo an integer      8
Resolvent operator      362
Rest mass      242
Rest-energy      242
Restriction of map to a subset      12
Reversible process      458
Ricci identities      514
Ricci identities general      515
Ricci scalar      526
Ricci tensor      526
Riemann tensor      see “Curvature tensor” “Riemann
Riemannian manifold      469
Riesz representation theorem      342 369
Riesz — Fischer theorem      333
Right action      50
Right translation      51 278 559
Rigid body      472
Ring      59
Robertson — Walker models      549 582
Robertson — Walker models flat      549
Robertson — Walker models open      550
Robertson — Walker models, closed      549
Rotation      53
Rotation group      38 53
Rotation group spinor representation      174
Rotation operator      392
Saddle point      118
scalar      60
Scalar multiplication      61
Scalar potential      248
Scalar product      133
Schmidt orthonormalization      138 335
Schrodinger equation      379
Schrodinger equation time-independent      383
Schrodinger picture      380
Schur’s lemma      124
Schwarzschild radius      545
Schwarzschild solution      545
Sectional curvature      532
Segre characteristics      114
Self-adjoint      348
Self-adjoint operator      141
Semi-direct product      57
Semigroup      18
Semigroup homomorphism      19
Semigroup identity element      18
Semigroup isomorphism      19
Separable      332 335
Separation axioms      269
SEQUENCE      13
Set      2
Set theory      3
shift operators      344 347 353
Similarity transformation      43 86
Simple function      290
Simultaneity      236
Simultaneous events      54
Singleton      4
Singular chains      489
Singular p-simplex      496
Smooth vector field      422
Smooth vector field along a parametrized curve      424
Smooth vector field on open set      424
Source field      246
Space of constant curvature      532 534 580
Space-time      536
Spacelike 3-surface      251
Spatial inversion      393
Special linear group      37
Specific heat      464
Spectral theorem hermitian operators      356
Spectral theorem self-adoint operaotrs      363
Spectral theory unbounded operators      362—364
Spectrum bounded operator      353—357
Spectrum continuous spectrum      353
Spectrum point spectrum      353
Spectrum unbounded operator      362
Spherical pendulum      471
Spherical symmetry      542 583
Spin-statistics theorem      397
Standard n-simplex      494
State      369
State, dispersion-free      371
Static metric      585
Stationary metric      585
Step function      290
Stereographic projection      413
Stern — Gerlach experiment      368
Stokes’ Theorem      487 491
Strange attractors      22
Stronger topology      261
Structure constants      150
Structured set      9
Subalgebra      151
Subcovering      271
Subgroup      28
Subgroup, conjugate      43
Subgroup, generated by a subset      278
Subgroup, normal      46
Subgroup, trivial      28
Subrepresentation      121
Subset      5
Subspace dense      357
Subspace Hilbert      335
Subspace, generated by a subset      72 335
Subspace, spanned by a subset      72
Sum of vector subspaces      67
Summation convention      81
Superposition of polarization states      367
Superset      5
Support of a function      309
Support of an n-form      484
Surface of revolution      534
Surjection      11
Surjective map      11
Sylvester’s theorem      130
Symmetric group      30
Symmetric relation      8
Symmetrical state      397
Symmetrization operator      405
Symmetry group of a set of functions      53
Symmetry group of Lagrangian system      474
Symmetry transformation between observers      387
Symplectic groups      39
Symplectic manifold      475

Symplectic structure      475
Tangent 4-vector      239
Tangent bundle      424
Tangent map      426
Tangent space at a point      418
Tangent vector at point m a manifold      418
Tangent vector components      420
Tangent vector to a curve at a point      420
Temperature      404
Tensor      180
Tensor antisymmetric part      205
Tensor contraction      198
Tensor contravariant of degree      2 181 190
Tensor covariant of degree      2 181 187
Tensor mixed      192
Tensor of type (r,s)      186
Tensor of type (r,s) at a point      421
Tensor product      194
Tensor product of covectors      187
Tensor product of dual spaces      186
Tensor product of two vector spaces      179
Tensor product of two vectors      179
Tensor product of vector spaces      186
Tensor product of vectors      190
Tensor symmetric      189 201
Tensor, antisymmetric      201 204
Tensor, components of      188 190 194
Test functions      309
Test functions of order m      309
Test particle      536
Thermal contact      458
Thermal equilibrium      458
Thermal variable assumption      459
Thermodynamic system equilibrium states of      457
Thermodynamic system internal variables      457
Thermodynamic system number of degrees of freedom      457
Thermodynamic system thermal variables      457
Thermodynamic variables      457
Tidal forces      536 539
Time dilatation      237
Time translation      392
Time-reversal operator      394
Topological group      277
Topological group, discrete      277
Topological invariant      263
Topological manifold      411
Topological product      266
Topological space      258
Topological space compact      271
Topological space connected      273
Topological space disconnected      273
Topological space first countable      262
Topological space Hausdorff      269
Topological space locally connected      278
Topological space normal      265
Topological space second countable      262
Topological space separable      262
Topological subgroup      277
Topological subspace      259
Topological vector space      279
Topologically equivalent      263
topology      21 257
Topology by identification      268
Topology generated by a collection of sets      261
Topology, induced      265 266
Torsion 2-forms      527
Torsion map      512
Torsion tensor      512—513
Torus, n-torus      415
Total angular momentum      385
Total order      9
Trace      107
Transformation group      30
Transformation of a manifold      433
Transformation of a set      12
Transformation of velocities Newtonian      229
Transformation of velocities relativistic      237
Transition functions      411
Transitive action      50 572
Transitive relation      8
Translation operators      391
Transmission probability      367
TRANSPOSE      37
Transpose of a linear operator      96
Triangle inequality      137 264 330
Trivial topology      261
Unary relation      7
Uncountable set      14
Unimodular group      37
Unimodular group complex      39
Union of sets      5
Unit matrix      36
Unitary group      40
Unitary group special      40
Unitary operator eigenvalues      352
Unitary operator eigenvectors      352
Unitary transformation      139
Variables      3
Variation field      466
Variation of a curve      465
Variation of fields      553
Variational derivative      553
Vector      60
Vector addition      61
Vector field on a manifold      422
Vector field parallel along a curve      508
Vector field, complete      434
Vector product      220
Vector space      60
Vector space finite dimensional      72
Vector space homomorphism      63
Vector space infinite dimensional      72
Vector space isomorphism      63
Vector subspace      66
Volume element      215
Volume element on a manifold      481
Vortex point      118
Wave equation Green’s function      326—328
Wave equation inhomogeneous      326
Wave operator      248
Weak field approximation      537
Weaker topology      261
Wedge product      208
Weierstrass approximation theorem      337
Wigner’s theorem      388
Work done by system      458
Work done on system      458
Work form      459
World-line      239 536
Zero vector      61
Zeroth law of thermodynamics      458

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