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

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-symbol      215
$\sigma$-algebra      287
$\sigma$-algebra generated      288
$\varphi$-related vector fields      560
1-form      90 420
1-form components of      421
1-form exact      428
2-torus      9
2-vector      161
2-vector simple      161
3-force      242
3-sphere      530
4-acceleration      241
4-current      246
4-force      242
4-momentum      242
4-scalar      232
4-tensor      228
4-tensor 4-covector      232
4-tensor field      244
4-tensor of type (r,s)      232
4-vector      232
4-vector future-pointing      233
4-vector magnitude of      233
4-vector null      233
4-vector past-pointing      233
4-vector spacelike      233
4-vector timelike      233
4-velocity      241
Aberration of light      238
Absolute continuity      356
Absolute entropy      463
Absolute gas temperature      458
Absolute temperature      463
Absolute zero of temperature      463
Accumulation point      260
action      465 554
Action of Lie group on a manifold      572
Action principle      554
Addition modulo an integer      29
Addition of velocities Newtonian      229
Addition of velocities relativistic      238
Additive group of integers modulo an integer      29
Adiabatic enclosure      458
Adiabatic processes      458
Adjoint representation of a Lie algebra      577
Advanced time      546
Affine connection      see “Connection”
Affine space      231
Affine space coordinates      231
Affine space origin      231
Affine space, difference of points in      231
Affine transformation      54 58
Algebra      149
Algebra homomorphism      150
Algebra isomorphism      151
Algebra, associative      149
Algebra, commutative      149
Almost everywhere      135 299
Alternating group      33
Angular 4-momentum      252
Angular momentum operator      392
Angular momentum orbital      385
Angular momentum spin      385
Annihilator of a subset      95
Annihilator subspace      454
Anti-homomorphism      50
Anti-unitary transformation      388
Antidenvation      214 448
Antilinear      134
Antilinear transformation      388
Antisymmetrical state      397
Antisymmetrization operator      205 405
Associative law      11 27
Atlas      412
Atlas, maximal      412
Automorphism inner      278
Automorphism of groups      42
Autonomous system      118
Axiom of extensionality      4
Banach space      282
Basis      73
Bayes’ formula      294
Bessel’s inequality      336
Betti numbers      497
Bianchi identities      see “Bianchi identity” “Second
Bianchi identities first      514 529
Bianchi identities second      515 526 529
Bianchi types      582
Bijection      11
Bijective map      11
Bilinear      127 181
Binary relation      7
Bivector      161
Block diagonal form      107
Boost      236
Borel sets      288
Bose — Einstem statistics      397
Boson      397
Boundary      496
Boundary map      487
Boundary of a p-chain      495
Boundary of a set      260
Bounded above      17
bounded linear map      283
Bounded set      273
Bra      369
Bra-ket notation      342 369
Bracket product      167
Canonical 1-form      478
Canonical commutation relations      372
Canonical map      12
Cantor set      15 299
Cantor’s continuum hypothesis      16
Cantor’s diagonal argument      15
Caratheodory      460
Cardinality of a set      13
Cartan formalism      527—534
Cartan’s first structural equation      528
Cartan’s lemma      213
Cartan’s second structural equation      523
Cartesian product      266
Cartesian product of two sets      7
Cartesian tensors      201 228
Category      23
Category of sets      23
Cauchy sequence      265
Cauchy — Schwartz inequality      136 336
Cayley — Hamilton theorem      105
Cellular automaton      22
Centre of a group      46
Certainty event      293
Character of a representation      147
Characteristic equation      102
Characteristic function      12
Characteristic polynomial      102
Charge density      245
Charge density proper      245
Charge flux density      245
Charts having same orientation      481
chemical potential      407
Christoffel symbols      519
Clifford algebra      158
Closed set      259
Closed subgroup      277
Closed subgroup of a Lie group      569
Closure of a set      260
Closure of vector subspace      335
Closure property      27
Coarser topology      261
Coboundary      497
Cochains      497
Cocycle      497
Codimension      79
Cohomologous cocycles      498
Collection of sets      4
Commutator      167
Commutator of observables      371
Commutator of vector fields      432
Compact support      309
Compatible charts      412
Complementary subspaces      67
Complete orthonormal set      see “Orthonormal basis”
Completely integrable      455
Complex number      152
Complex number, conjugate of      153
Complex number, inverse of      153
Complex number, modulus of      153
Complex structure on a vector space      155
Complexification of a vector space      154
Component of the identity      278
Components of a linear operator      76
Components of a vector      75
Composition of maps      11
Conditional probability      293
Configuration space      469
Conjugacy class      43
Conjugation by group element      43
Connected component      275
Connected set      273
Connection      507
Connection 1-forms      527
Connection Riemannian      518
Connection symmetric      see “Connection” “Torsion-free”
Connection torsion-free      513
Connection vector field      522
Conservation of charge      252
Conservation of total 4-momentum      244
Conservative system      468
Conserved quantity      393
Constant of the motion      393
Constants      2
Constrained system      468
Constraint      468
Contact 1-form      479
Contact transformation, homogeneous      479
Continuous function      257 262
Continuous spectrum      363
Contracted Bianchi identities      527
Contravariant degree      186
Contravariant transformation law of components      84
Convergence to order m      310
Convergent sequence      255 256 260 280
Conway’s game of life      23
Coordinate chart      411
Coordinate functions      411
Coordinate map      411
Coordinate neighbourhood      411
Coordinate system at a point      411
Coordinates of point in a manifold      411
Correspondence between classical and quantum mechanics      382
Correspondence principle      375
Coset left      45
Coset of a vector subspace      69
Coset right      46
Cosmological constant      582
Cosmology      548
Cotangent bundle      424
Cotangent space      420
Countable set      13
Countably infinite set      13
Countably subadditive      295
Covanant derivative      507
Covanant derivative of a tensor field      510
Covanant derivative of a vector field      507
Covanant derivative of a vector field along a curve      508
Covanant derivative, components of      508
Covariant degree      186
Covariant vector transformation law of components      94
Covector at a point      420
Covector field      423
Covectors      90
Covering      271
Covering open      271
Critical point      118
Cubical k-chain      486
Current density      245
Curvature 2-forms      528
Curvature tensor      513 516
Curvature tensor physical interpretation      537—539
Curvature tensor Riemann curvature tensor      524
Curvature tensor Riemann curvature tensor number of independent components      526
Curvature tensor Riemann curvature tensor symmetries of      524
Curve directional derivative of a function      417
Curve passes through a point      416
Curve smooth parametrized      416
Curves, one parameter family of      522
CYCLE      496
de Rham cohomology spaces (groups)      498
de Rham’s Theorem      499
de Sitter universe      582
Delta distribution      312
Delta distribution, derivative of      316
Dense set      261
Dense set in $\mathbb{R}$      14
Density operator      398
Diathermic wall      458
Diffeomorphic      416
Diffeomorphism      416
Difference of two sets      6
Differentiable 1-form      423
Differentiable manifold      412
Differentiable structure      412
Differentiable vector field      422
Differential exterior algebra      447
Differential of a function      423
Differential of a function at a point      421
Differential r-form      447
Differential r-form, closed      497
Differential r-form, exact      497
Dimension of vector space      72
Dirac delta function      308 353
Dirac delta function change of variable      318
Dirac delta function Fourier transform      320
Dirac measure      293
Dirac string      504
Direct product of groups      48
Direct sum of vector spaces      67
Discrete dynamical structure      22
Discrete dynamical system      18
Discrete symmetries      393
Discrete topology      261
Disjoint sets      6
Displacement of the origin      390
distribution      311—315
Distribution density      312
Distribution of order m      311
Distribution regular      311
Distribution singular      312
Distribution tempered      321
Distribution, derivative of      315
Distribution, Fourier transform of      321
Distribution, inverse Fourier transform of      321
Distributive law      59 149
Divergence-free 4-vector field      245
Division algebra      153
Domain of a chart      411
Domain of a mapping      10
Domain of an operator      357
Dominated convergence      306
1 2 3 4
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