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Felsager B. — Geometry, particles and fields
Felsager B. — Geometry, particles and fields



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Название: Geometry, particles and fields

Автор: Felsager B.

Аннотация:

This second edition of Geometry, Particles and Fields is a direct reprint of the first edition. From a review of the first edition: "The present volume is a welcome edition to the growing number of books that develop geometrical language and use it to describe new developments in particle physics...It provides clear treatment that is accessible to graduate students with a knowledge of advanced calculus and of classical physics...The second half of the book deals with the principles of differential geometry and its applications, with a mathematical machinery of very wide range. Here clear line drawings and illustrations supplement the multitude of mathematical definitions. This section, in its clarity and pedagogy, is reminiscent of Gravitation by Charles Misner, Kip Thorne and John Wheeler...Felsager gives a very clear presentation of the use of geometric methods in particle physics...For those who have resisted learning this new language, his book provides a very good introduction as well as physical motivation. The inclusion of numerous exercises, worked out, renders the book useful for independent study also. I hope this book will be followed by others from authors with equal flair to provide a readable excursion into the next step." PHYSICS TODAY Bjoern Felsager is a high school teacher in Copenhagen. Educated at the Niels Bohr Institute, he has taught at the Universities of Copenhagen and Odense.


Язык: en

Рубрика: Физика/Классическая физика/Классические поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1983

Количество страниц: 643

Добавлена в каталог: 14.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
k-form      327
Kink      137
Kink sector      138
Klein — Gordon equation      95
Klein — Gordon field      95—98 427—428
Kronecker delta      315
Lagrange multiplier      571
Lagrangian density      86
Lagrangian density for the electromagnetic field      100
Lagrangian density for the Klein — Gordon field      95
Lagrangian formalism and the exterior calculus      424—429
Lagrangian formalism for a monopole      482—486
Lagrangian formalism for a point particle      32—38
Lagrangian formalism for a relativistic particle      295
Lagranglan formalism for a relativistic string      442—444
Lagrangzan formalism for a relativistic field      86—90
Laplace's equation in 2-space      556—557
Laplacian in 3-space      5
Laplacian on a manifold      363 422
Legendre transformation      202
Leibniz' rule in $R^3$      372
Leibniz'rule for differential forms      340
Levi-Civita form      350
Levi-Civita symbol      348 350
Light cone      281
Light cone coordinates      150
Line element      293
Line-integral      6 415
Linearized equations of fluctuations      153
Linearly polarized light      105
Liouville's theorem      561
Locally finite family of functions      405
Lorentz force      4
Lorentz group      287
Lorentz transformation      287
Lorenz gauge      10
Loreritz force in quantum mechanics      50 53—55
Loreritz force, generalized      474
Loreritz matrix      287
Magenetic charge      469—470 472
Magnetic current      471—472
Magnetic flux      11—14 429 432
Magnetic monopole      13—14 318—320 381—384 469—503
Magnetic string in a superconductor      78 437—441
Magnetic string in the abelian Higgs' model      448—449
Manifold      258
Manifold defined by an equation of constraint      268
Massive vector field      107—108 112—113 428
Massless field theories      622
Maximal atlas      257
Maxwell field      22 428
Maxwell's equations      5 376 381 428
Maxwell's equations including monopoles      472
Mehler's formula      179
Meissner effect      72 435
Metric      276—284
Metric components      277
Metric energy-momentum tensor      615
Metric on a sphere      281—283
Metric on Minkowski space      288—289
Metric, reciprocal components      278
Minimal coupling      69 117 621
Minkowski metric      280
Minkowski space      284—290
Mixed tensor      312
Moebius strip      346
Momentum density      24
monopole      13—14 318—320 381—384 469—503
Monopole confinement      450
Monopole in the abelian Higgs' model      449—450
Multi-soliton solution in the sine-Gordon model      153
Multilinear map      308
Nambu string      442—445 452—454
Nielsen — Olesen vortex      448 453
Node-theorem for eigenfunctions in the discrete spectrum      157
Noether's theorem      602—606
Noether's theorem for internal symmetries      605
Noether's theorem for scalar fields      604
Noether's theorem for vector fields      613
Non-linear field theories      94 127—131
Non-pertubative sector      132
Null-geodesic      537
Null-vector      281
Odd form      332
One-parameter family of diffeomorphisms      601
One-parameter group of isometries      593—594
One-parameter group of unitary transformations      593
One-point compactification of the Euclidean space      541
Order parameter in a ferromagnet      570
Order parameter in a superconductor      432
Orientability of a boundary      401
Orientability of a manifold      345
Orientability of a regular domain      401
Ortochronous Lorentz transformation      288
Paracompact      406
Partial integration      413
Partition of unity      406
path integral      42
Path integrals and determinants      194
Path-cam-trace integral      199
Pauli's exclusion principle      73
Penetration length      435
Phase ambiguity in the path integral      180—181
Planck mass      621
Plane wave      135
Poincare group      539
Poincare transformation      285 286 538—539 607
Poincare's lemma for the co-differential      360
Poincare's lemma for the exterior derivative      338
Poincare's lemma for weak forms      460
Poincare's lemma in $R^3$      372
Poisson bracket for point particles      67
Poisson bracket for relativistic fields      92
Polarization vector for the electro-magnetic field      100
Primitively harmonic form      365 422
Probability amplitude      39—40
Product manifold      264—265
Proper Lorentz transformation      288
Proper time      293
Pseudo-orthogonal group      546
Pseudo-orthogonal matrix      546
Pseudo-Riemannian manifold      280
Pseudo-Tensor      350
Pseudo-vector      3
Pull-back of convectors      521
Pull-back of cotensors      522
Pull-back of differential forms      523
Pull-back of equivalent tensors      534
Pull-back of integrals      528
Pull-back of metrics      522—523
Quadratic Lagrangian      45 194—198
Quantization of the magnetic charge      500—502
Quark      450
Quark confinement      451
Quark potential      452
Quasi-static solution in a non-linear field theory      143
Rainbow angle      509
Rank of a cotensor      308
Rank of a mixed tensor      312
Rapidity      609
Regge trajectory      445
Regular domain      397 460
Regular value      515
Regularity of a smooth map      515
Relativistic string      442
Restriction of a differential form      408
Riemann sphere      560
Riemannian manifold      280
Sard's theorem      519
Scalar field      274—275
Scalar product between differential forms      357—359
Scale associated with a diffeomorphism      625
Scale current      624
Scale invariance in a relativistic field theory      618—624
Scale invariance of minimal coupling      620—621
Scale transformation in a relativistic field theory      158—159 581—582 618
Scaling dimension of a scalar field      619
Scaling dimension of a vector field      620
Schroedinger equation      32
Schroedinger equation in the canonical formalism      68
Schroedinger equation in the path-integral formalism      62—64
Schroedinger wave function      41 55—61
Schwinger formalism for monopoles      492
Self-dual form      355
Self-duality equation      554—558
Self-duality equation in a ferromagnet      574
Self-duality equation in the exceptional $\phi^4$-model      579
Simple form      342
Simple manifold      258
Sine-Gordon equation      128
Sine-Gordon model      128—129
Singular differential form      454
Singular gauge transformation      18 384
Skew-symmetrization      328—329
Slit experiment      39—40 49—55
Smooth map between manifolds      512
Smooth map in an Euclidean space      252
Solenoid      15—19 52 78—79 306—307
Soliron versus instanton      217
Solitary wave      135
Soliton      144
Soliton-soliton scattering      145—147
Soriau's formula for the propagator of a harmonic oscillator      181
Space like geodesic      537
Space like vector      281
Space slice      431
Special conformal transformation      533
Special relativity, basic assumptions      286
Spectrum of the angular momentum in the Dirac formalism      497
Spectrum of the angular momentum in the Schwinger formalism      496—497
Spectrum of the Eckhardt potential      163
Spectrum of the Schroedinger operator      157
Sphere (as a manifold)      259—264 281—283
Spherical symmetry in Minkowski space      289—290
Spin of a photon      103
Spin of a vector field      610—611
Spin of a vector particle      598
Spin wave in a ferromagnet      573
Spinning string      444—445
Standard coordinates on a manifold defined by an equation of constraint      267
Standard coordinates on a sphere      261
Standard Lorentz transformation      288
Static solution in a non-linear field theory      138—140
Stationary phase approximation      205
Stationary state      71
Stokes' theorem in 3-space      6
Stokes' theorem on a manifold      411
Stratification      334
Submanifold      395
Submersion      518
Superconductivity      72—79 432—441
Symmetry transformation in field theory      601
Symmetry transformation in quantum mechanics      595—596
Tangent space      272
Tangent vector      269—276
Tensor      312
Tensor field      314
Tensor product      310
Tidal force      299
Time-dependent oscillator      188
Time-evolution operator      169
Time-like curve      291
Time-like geodesic      537
Time-like vector      281
Topological charge      133—135
Topological conservation law      134
Topological current      134
Torus (as a product manifold)      265
Transition function      255
Transport of tangent vectors      512—515
Transport of tensors      524—525
Travelling wave      136
True energy-momentum tensor      89 611—613
Tube lemma      587
Unit tensor field      315
Unitary group      58
Unitary matrix      58
Unitary transformation      498
Vacuum sector      132
Vacuum texture      440
Vacuum, classical      130
Vector field      275
Vector particle      594—595
Velocity vector      270
Virial theorem in (1+1)-dimensional space-time      159
Virial theorem in the exceptional $\phi^4$-model      582
Volume expansion      625
Volume form      343—344 351
Volume form on a sphere      567
Volume of a regular domain      414
Vortex-string in a superconductor      78 441
Wave equation      557
Weak coupling approximation      199
Weak k-form      458
Wedge product in 3-space      6
Wedge product of differential forms      330
Weierstrass' theorem      561
Wick rotation      212
Winding number      564
WKB-approximation      204—209
World-line      284
World-sheet      442
wronskian      241—242
Yukawa-potential      97
Zero mode in quantum mechanics      238
Zero-mode in a non-linear field theory      158
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