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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
$\delta$-(delta-) function in Euclidean space      18
$\delta$-(delta-) function on a manifold      455
$\phi^4$-(phi-to-the-fourth) model      127
Abelian gauge theory      58
Abelian Higgs' model      445—50
Abraham's theorem      27 589 591—592
Abrikosov vortex      78
Action of a point particle      33
Action of a relativistic field      86
Action of a relativistic particle      294
Action of a relativistic string      443
Adapted coordinate system      396
Affine parameter on a geodesic      535
Ampere's law      5
angular momentum      28
Angular momentum of a charged particle in a monopole field      489—490
Angular momentum of a relativistic string      444
Angular momentum of an electromagnetic field created by a charge—monopole pair      487
Angular momentum operators for a charged particle in a monopole field      492—493 495
Approximative ground state      142
Arc-length      291
Atlas      256
Baecklund transformation      150
Bag      451
Basic form      333—336
BCS-theory of superconductor      73
Bianchi's permutability theorem      151
Bion      148
Bloch wave      235
Bogomolny decomposition      140
Bogomolny decomposition in a (1+1)-dimensional scalar field theory      141
Bogomolny decomposition in a ferromagnet      573
Bogomolny decomposition in the exceptional $\phi^4$-model      580
Bohm — Aharonov effect      49—53 78—79 502
Bohr — Sommerfeld quantization rule      200 203
Bosonic spectrum of a charged particle in a monopole field      496 497
Bound states (in the sine-Gordon model)      148—149
Boundary      398
Bracket      595
Breather      147
Brouwer degree      564
Brouwer's lemma      564
Brouwer's theorem      566
Canonical energy-momentum tensor      89
Canonical frame vectors in the dual space      303
Canonical frame vectors in the tangent space      270
Canonical identification of mixed tensors      316—317
Canonical identification of tangent vectors and convectors      305—306
Canonical quantization of point particles      68—72
Canonical quantization of relativistic fields      93
Canonical system      65
Cartan's Lemma      399
Cauchy problem      109—113
Cauchy — Riemann's equations      365 555
Caustic      173
Characteristic line on a null cone      542
Characteristic vector field associated with a one-parameter family of diffeomorphisms      594 601
Charge conservation      7 119—121
Charge rotation      474—475
Charged field      116—119
Christoffel field      295 373
Circularly polarized light      106
Classical approximation of a propagator      44
Classical vacuum      130
Closed domain      400
Closed form      341
Co-closed form      364
Co-differential      360—362 421—422
Co-differential of a weak form      459
Co-exact form      364
Coherence length      433—434
Coleman's formula for a quadratic path integral      195
Colour field      451
Commutation rules for wedge products      331—332
Commutative diagram      256
Compact subset of an Euclidean space      263
Complex coordinate system      560
Complex Klein — Gordon field      113—116
Complex manifold      560
Complex valued differential form      365
Composite particles in non-linear field theories      160—164
confinement      450—451
Conformal compactification of a pseudo-cartesian space      546
Conformal compactification of an Euclidean space      541
Conformal energy-momentum tensor      624
Conformal group      547—551
Conformal invariance in field theories      625—632
Conformal invariance of Maxwell's equations      558
Conformal invariance of the self-duality equation      555
Conformal map      531—533
Conformal map on the sphere      559—561
Conjugate momentum of a point particle      65
Conjugate momentum of a relativistic field      90
Conservation law, topological      134
Conservation laws      587—592
Conservation laws associated with conformal symmetry      613 631—632
Conservation of angular momentum in field theories      609—611
Conservation of angular momentum in quantum mechanics      597—600
Conservation of electric charge      588—589
Conservation of energy and momentum      5895—92 614—618
Conservation of momentum in field theories      608
Conservation of momentum in quantum mechanics      596—597
Constraint equation (in gauge theory)      111
Continuity equation      7 21 381
Contraction of differential forms      356 359
Contraction of tensors      310
Contravariant components of a tangent vector      272 306
Contravariant quantity      274
Cooper current      75
Cooper pair      73
Coordinate line      270
Coordinate system      254
Corectot      300—305
Correspondence principle in quantum mechanics      205
Cotensor      308
Coulomb field      14 456—457
Covariant components of a tangent vector      306
Covariant quantity      274
Critical value      515
Cross section for scattering in a monopole field      506—509
Cross-product      3 351—352 366
Curl      5 366
Cyclic coordinates      307 383
Cylinder (as a product manifold)      265
Cylindrical coordinates      290
d'Alembertian      20
Decomposition of cotensors      311
Decomposition of differential forms      332
Degree of a smooth map      563
Derrick's scaling argument for scalar field theories      158—159
Derrick's scaling argument for the exceptional $\phi^4$-theory      581—582
Determinant of a differential operator      194
Determinant of a metric      279 348
Determinantal relation      196 197—198
Diffeomorphism      515
Differentiable manifold      258
Differentiable structure      257 258
Differential      304
Differential form      336
Dilatation      533
Dilute gas approximation      233
Dirac formalism for monopoles      493
Dirac string      18 383—384 476—481
Dirac's action for a system including monopoles      482
Dirac's commutation rule for the angular momentum operators      493
Dirac's lemma      480
Dirac's quantization rule for the magnetic charge      487
Dirac's theorem      482
Dirac's veto      478
dispersion relation      84 90
distribution      458
Divergence      5 366
Double dualisation      354—355
Double square well      220—222
Dual map      352—355 551—554
Dual map in $R^3$      367
Dual map in Minkowski space      374
Dual map of a weak form      460
Dual vector space      301
Dyon      470
Eckhardt potential      162
Edge condition for a relativistic string      444
Einstein — deBroglie rule      48
Electric current in a gauge theory      120
Electric flux      429 430 432
Embedding      518
Energy current      24 88
Energy density      24 87
Energy split in a double well      232 245
Energy-momentum tensor      22—28 320—321
Energy-momentum tensor of a point particle      23
Energy-momentum tensor of electromagnetic field      26 99—100 320
Energy-momentum tensor of massive vector field      108
Energy-momentum tensor, canonical      88—89
Energy-momentum tensor, conformal      624
Energy-momentum tensor, metric      615
Energy-momentum tensor, true      89 611—613
Equation of constraint      111
Equation of continuity      7 21 381
Euclidean action      213
Euclidean group of motions      539
Euclidean metric      280
Euclidean propagator      212 214—216
Euclidean vacuum      216
Euler — Lagrange equation for a point particle      33 35
Euler — Lagrange equation for a relativistic field      87 91
Euler — Lagrange equation on covariant form      425
Even form      332
Exact form      341
Exceptional $\phi^4$-model      578—582
Exterior derivative      336—342
Exterior derivative in $R^3$      371
Exterior derivative in Minkowski space      375
Exterior derivative of a differential form      337
Exterior derivative of a function      302
Exterior derivative of a weak form      459
Extrinsic coordinates of a tangent vector      271
Faraday's law      5
Fermiohio spectrum of a charged particle in a monopole field      497
Ferromagnet      570
Feynman — Soriau's propagator for the harmonic oscillator      181 187
Feynman's formula for the path-integral      182
Feynman's principle of the democratic equality of all histories      43 93
Feynman's propagator      42 167—172
Feynman's propagator in canonical formalism      71
Feynman's propagator in momentum space      171—172
Feynman's propagator of a free particle      46
Feynman's propagator of a harmonic oscillator      174 181
Feynman's propagator of a timedependent oscillator      188—193
Fictitious forces      296 299
Field quantum in a free field theory      89—90
Field quantum in a non-linear field theory      94 130—131
Fine-structure constant      621
Flux integral      416
Flux-quantization in superconductors      77—78 502—503
Four-velocity      293
Free field theories      89—90
Free particle wave function      49
Functional derivative      91
Galilei's principle      298
Gauge covariant derivative      60 69
Gauge group (in electromagnetism)      57
Gauge phase factor      50
Gauge potential      7—11 381
Gauge scalar      59
Gauge theory of electrically charged fields      116—118
Gauge theory, basic ingredients      61
Gauge transformation      10 498—499
Gauge transformation of the action      38
Gauge transformation of the first and second kind      118
Gauge transformation of the propagator      56
Gauge transformation of the Schroedinger wave function      55—57
Gauge transformation on covariant form      307 381
Gauge vector      58
Gauss' law in electromagnetism      5
Gauss' theorem in 3-space      6
Gauss' theorem on a manifold      417
Gaussian approximation of the path integral      238
Geodesic      296 535—538
Geodesic equation      296 535
Ginzburg — Landau parameter      436
Ginzburg — Landau theory for superconductivity      432
Gradient      5 366
Gravitational forces      299—300
Green's identities      423
Ground state for a double well      232
Ground state for a harmonic oscillator      178
Ground state for a non-pertubative sector      38—43
Ground state for a periodic potential      235
Ground state in quantum mechanics      219—223
Group property for the propagator      46
Hadron      445 450
Hamilton's equations for a point particle      66
Hamilton's equations for a relativistic field      90 92
Hamilton's principal function      200
Hamiltonian      65
Hamiltonian density      87
Hamiltonian formalism for a point particle      65—68
Hamiltonian formalism for a relativistic field      90—94
Harmonic form      364 422
Heat operator      214
Heaviside function      18
Heisenberg's commutation rules for a point particle      71
Heisenberg's commutation rules for a relativistic field      93
Heisenberg's model for a ferro-magnet      570
Heisenberg's uncertainty principle      176
Helicity of a photon      104
Hermite polynomials      179
Hermitian operator      70
Higg's field      445
Hilbert product of differential forms      420
Hodge duality      354
Holomorphic function      365 555—556 560
Holomorphic map      560
Holomorphic map on a sphere      561
Homeomorphism      252
Honey-comb structure      334—335
Immersion      517
Impact parameter      490
Implicit function theorem      266
Induced metric      282
Inertial coordinates      285
Inertial frame of reference      285
Infinitisemal generator for a one-parameter group of unitary transformations      593—595
Infinitisemal propagator      64
Instanton      216
Instanton gas      232
Instanton in quantum mechanics      217—219
Instanton, relationship with tunnel effect      223—225
Integral of a differential form      403—411
Integral of a scalar field      413
Integral of a simple form      418—420
Interior of a regular domain      397
Internal symmetry      116 605
Intrinsic coordinates of a tangent vector      272
Intrinsic spin of a charged particle in a monopole field      495
inversion      533 540
Isometry      530
Isometry group on a manifold      538
Jacobi matrix      252
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