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.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 600

Добавлена в каталог: 05.10.2005

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Предметный указатель

Linear transformation      36 65
Linearized approximation      539
Linearly dependent set of vectors      73
Linearly independent vectors      73
Local flow      434
Locally Euclidean space      411
Locally Euclidean space dimension      411
Locally flat space      532—534
Locally integrable function      311
Logical connectives      3
Logical propositions      3
Logistic map      22
Lorentz force equation      247
Lorentz gauge      248
Lorentz gauge, gauge freedom      248
Lorentz group      56
Lorentz transformation      56
Lorentz transformation improper      230
Lorentz transformation proper      230
Lorentz — FitzGerald contraction      237
Lowering an index      200
Magnetic field      246
Magnitude of a vector      127
MAP      10
Map differentiable at a point      416
Map differentiable between manifolds      415
Mapping      10
Mass of particle      467
Matrix adjoint      40
Matrix components of      36
Matrix element of an operator      347
Matrix group      37
Matrix improper orthogonal      38
Matrix Lie groups      169—172 570
Matrix of components      98
Matrix of linear operator      76
Matrix unimodular      37
Matrix, non-singular      36
Matrix, orthogonal      38
Matrix, proper orthogonal      38
Matrix, symplectic      39
Matrix, unitary      40
Maurer — Cartan relations      563
Maximal element      17
Maximal symmetry      579
Maxwell 2-form      502
Maxwell equations      246
Maxwell equations source-free      246
Measurable function      289—292
Measurable set      287
Measurable space      288
Measure      292
Measure complete      300
Measure space      287 292
Metric      264
Metric space      264
Metric space complete      265
Metric tensor      189 469 516
Metric tensor inverse      516
Metric topology      264
Michelson — Morley experiment      229
Minimal annihilating polynomial      105
Minkowski space      55 230 231 535
Minkowski space inner product      233
Minkowski space interval between events      232
Minkowski space-time      230
Mixed state      399
Mixed state stationary      400
Module      63
Momentum 1-form conjugate to generalized velocity      472
Momentum operator      361 375
Monotone Convergence Theorem      302
Morphism      23
Morphism, composition of      23
Morphism, epimorphism      24
Morphism, identity morphism      23
Morphism, isomorphism      25
Morphism, monomorphism      24
Multilinear map      186
Multiplication operator      345 347 350 353
Multiplicities of representation      147
Multivector      183 208
Multivectors      163
n-ary function      11
n-ary function arguments      11
n-ary relation on a set      7
Natural numbers      4
Negatively oriented      217
Neighbourhood      255 256 262
Newtonian tidal equation      540
Nilpotent matrix      110
Nilpotent operator      110
Node stable      118
Node unstable      118
Noether’s theorem      473
Non-degenerate 2-form      474
Norm bounded linear operator      350
Norm of a vector      135
Norm of linear operator      344
Normal coordmates      see “Geodesic coordinates”
Normed space complete      282
nth power of a linear operator      101
Null cone      233
Null vector      127
Nullity of a linear operator      80
Number of degrees of freedom of constrained system      468
Objects      23
Observable      370
Observable compatible      372
Observable complementary      372
Observable complete      370
Observable expectation value of      371
Observable root mean square deviation of      371
Occupation numbers      405
Octonians      158
Odd parity      394
One-parameter group of transformations      433
One-parameter group of unitary transformations      390
One-parameter subgroup      171
One-parameter subgroup of a Lie group      565
One-to-one correspondence between sets      11
One-to-one map      11
Onto map      11
Open ball      256 264
Open interval      255
Open map      278
Open neighbourhood      262
Open set      256 257
Open submanifold      413 430
Operator adjoint      346—348
Operator idempotent      348
Operator in Hilbert space      357
Operator projection      348
Operator, closed      358
Operator, densely defined      357
Operator, extension of      357
Operator, hermitian      348-349
Operator, invertible      345
Operator, isometric      349
Operator, normal      351
Operator, self-adjoint      360
Operator, symmetric      360
Operator, unbounded      357
Operator, unitary      349
Opposite orientation on a manifold      481
Oppositely oriented      217
Orbit      50
Orbit of a point under a Lie group action      572
Orbit of point under a flow      433
Ordered n-tuple      7

Ordered p-simplex      493
Ordered p-simplex vertices      493
Ordered pair      7
Orientable manifold      481
Orientation      217
Orientation on a manifold      481
Oriented manifold      481
Oriented vector space      217
Orthogonal 4-vectors      233
Orthogonal complement      341—342
Orthogonal complement of a vector subspace      142
Orthogonal groups      38
Orthogonal groups complex      39
Orthogonal groups proper      38
Orthogonal projection      341
Orthogonal vectors      127 137 341
Orthonormal basis      129 137 335 370
Outer measure      295
p-boundary on a manifold      496
p-chain      494
p-chain on a manifold      496
p-chain on a manifold boundary of      496
p-cycle on a manifold      496
Paracompact topological space      482
Parallel transport      509
Parallelogram law      140 330
Parametrized curve in Minkowski space      239
Parametrized curve null      239
Parametrized curve, length of      517
Parametrized curve, spacelike      239
Parametrized curve, timelike      239
Parity observable      394
Parseval’s identity      339
Partial order      9
Partially ordered set      9
Particle horizon      552
Particle number operator      359
Partition function canonical      402
Partition function grand canonical      406
Partition function one-particle      406
Partition of a set      8
Partition of unity subordinate to the covering      482
Pauli exclusion principle      397
Pauli matrices      173
Peano’s axioms      4
Perfect fluid      253
Perfect fluid pressure      253
Periods of an r-form      499
Permutation      30
Permutation cycle      31
Permutation cyclic      31
Permutation cyclic notation      31
Permutation even      32
Permutation group      30
Permutation interchange      32
Permutation odd      32
Permutation operator      395
Permutation parity      33
Permutation, order of      34
Permutation, sign of      33
Pfaffian system of equations      455
Pfaffian system of equations first integral      455
Pfaffian system of equations integral submanifolds      456
Phase space      478
Phase space, extended      479
Photon      242 367
Photon direction of propagation      242
Plane gravitational waves      547
Plane pendulum      470
Plane waves      366
Poincare group      56
Poincare transformation      56 230
Point spectrum      363
Poisson bracket      383 475
Poisson’s equation      323 534
Poisson’s equation Green’s function      323—325
Polarization circular      367
Polarization elliptical      367
Polarization linear      367
POSET      9
Position operator      360 375
Positively oriented      217
potential energy      468
Power set of a set      5
Poynting vector      253
Pre-Hilbert space      330
Principal pressures      253
Principle of equivalence      534—537
Probability measure      293
Probability of an event      293
Probability space      293
PRODUCT      18
Product of elements of a group      27
Product of linear maps      65
Product of manifolds      414
Product of vectors      149
Product topology      266
Projection map      11
Projection map tangent bundle      424
Projection operator      352
Projective representation      389
Proper time      241 536
Pseudo-orthogonal groups      39
Pseudo-orthogonal transformations      132
Pseudo-Riemannian manifold      516—522 529
Pseudo-Riemannian manifold, hyperbolic manifold      517
Pseudo-Riemannian manifold, Minkowskian manifold      517
Pseudo-Riemannian manifold, Riemannian manifold      516
Pseudo-sphere      582
Pullback      426
Pure state      399
Quantifiers      3
Quasi-static process      458
Quaternion      157
Quaternion inverse      158
Quaternion magnitude      158
Quaternion pure      157
Quaternion scalar part      157
Quaternion vector part      157
Quaternion, conjugate      157
Quaternions      157—158
Quotient vector space      69
r-forms      204
r-forms simple      212
r-vector      162 184 204
r-vector simple      162 211
Raising an index      200
range of a mapping      10
Range of an operator      357
Rank of a linear operator      80
Rational numbers      14
Ray      369
Ray representation      see “Projective representation”
Real inner product space      127
Real projective n-space      269
Real projective plane      269
Real structure of a complex vector space      155
Rectilinear motion      54
Refinement of an open covering      482
Refinement of an open covering, locally finite      482
Reflexive relation      8
Regular domain      489
Regular embedding      430
Regular k-domain      490
Regular value      353 362
Relative topology      259
Representation      120
Representation completely reducible      122
Representation equivalent      120
Representation faithful      320

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