Classical field theory: on electrodynamics, non-Abelian gauge theories, and gravitation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Schriftenreihe: | Graduate texts in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XII, 433 S. graph. Darst. |
| ISBN: | 9783642279843 9783642279850 |
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| 245 | 1 | 0 | |a Classical field theory |b on electrodynamics, non-Abelian gauge theories, and gravitation |c Florian Scheck |
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Datensatz im Suchindex
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|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 MAXWELL'S EQUATIONS 1
1.1 INTRODUCTION 1
1.2 GRADIENT, CURL AND DIVERGENCE 2
1.3 INTEGRAL THEOREMS FOR THE CASE O F M 3 7
1.4 MAXWELL'S EQUATIONS IN INTEGRAL FORM 11
1.4.1 THE LAW OF INDUCTION 11
1.4.2 GAUSS' LAW 13
1.4.3 THE LAW OF BIOT AND SAVART 15
1.4.4 THE LORENTZ FORCE 17
1.4.5 THE CONTINUITY EQUATION 18
1.5 MAXWELL'S EQUATIONS IN LOCAL FORM 21
1.5.1 INDUCTION LAW AND G A U S S ' L A W 22
1.5.2 LOCAL FORM O F THE LAW O F BIOT AND SAVART 23
1.5.3 LOCAL EQUATIONS IN ALL SYSTEMS OF UNITS 2 4
1.5.4 THE QUESTION OF PHYSICAL UNITS 25
1.5.5 EQUATIONS OF ELECTROMAGNETISM IN SI SYSTEM 28
1.5.6 THE GAUSSIAN SYSTEM O F UNITS 29
1.6 SCALAR POTENTIALS AND VECTOR POTENTIALS 35
1.6.1 A FEW FORMULAE FROM VECTOR ANALYSIS 35
1.6.2 CONSTRUCTION OF A VECTOR FIELD FROM ITS SOURCE AND ITS CURL 4 0
1.6.3 SCALAR POTENTIALS AND VECTOR POTENTIALS 42
1.7 PHENOMENOLOGY O F THE MAXWELL EQUATIONS 4 6
1.7.1 THE FUNDAMENTAL EQUATIONS AND THEIR INTERPRETATION . . 4 7 1.7.2
RELATION BETWEEN DISPLACEMENT FIELD AND ELECTRIC FIELD 5 0 1.7.3
RELATION BETWEEN INDUCTION AND MAGNETIC FIELDS . . . 52
1.8 STATIC ELECTRIC STATES 55
1.8.1 POISSON AND LAPLACE EQUATIONS 56
IX
HTTP://D-NB.INFO/1018211624
IMAGE 2
X
C O N T E N T S
1.8.2 SURFACE CHARGES, DIPOLES AND DIPOLE LAYERS 62
1.8.3 TYPICAL BOUNDARY VALUE PROBLEMS 66
1.8.4 MULTIPOLE EXPANSION O F POTENTIALS 69
1.9 STATIONARY CURRENTS AND STATIC MAGNETIC STATES 83
1.9.1 POISSON EQUATION AND VECTOR POTENTIAL 84
1.9.2 MAGNETIC DIPOLE DENSITY AND MAGNETIC MOMENT . . . . 84
1.9.3 FIELDS O F MAGNETIC AND ELECTRIC DIPOLES 88
1.9.4 ENERGY AND ENERGY DENSITY 92
1.9.5 CURRENTS AND CONDUCTIVITY 95
2 SYMMETRIES AND COVARIANCE O F THE MAXWELL EQUATIONS 97
2.1 INTRODUCTION 97
2.2 THE MAXWELL EQUATIONS IN A FIXED FRAME OF REFERENCE . . . . 97
2.2.1 ROTATIONS AND DISCRETE SPACETIME TRANSFORMATIONS . . . 98 2.2.2
MAXWELL'S EQUATIONS AND EXTERIOR FORMS 102
2.3 LORENTZ COVARIANCE O F MAXWELL'S EQUATIONS 119
2.3.1 POINCARE AND LORENTZ GROUPS 120
2.3.2 RELATIVISTIC KINEMATICS AND DYNAMICS 123
2.3.3 LORENTZ FORCE AND FIELD STRENGTH 126
2.3.4 COVARIANCE OF MAXWELL'S EQUATIONS 128
2.3.5 GAUGE INVARIANCE AND POTENTIALS 132
2.4 FIELDS O F A UNIFORMLY MOVING POINT CHARGE 136
2.5 LORENTZ INVARIANT EXTERIOR FORMS AND THE MAXWELL EQUATIONS . . 141
2.5.1 FIELD STRENGTH TENSOR AND LORENTZ FORCE 142
2.5.2 DIFFERENTIAL EQUATIONS FOR THE TWO-FORMS COF AND COJR . . 145
2.5.3 POTENTIALS AND GAUGE TRANSFORMATIONS 148
2.5.4 BEHAVIOUR UNDER THE DISCRETE TRANSFORMATIONS . . . . 149
2.5.5 * COVARIANT DERIVATIVE AND STRUCTURE EQUATION 150
3 MAXWELL THEORY AS A CLASSICAL FIELD THEORY 153
3.1 INTRODUCTION 153
3.2 LAGRANGIAN FUNCTION AND SYMMETRIES IN FINITE SYSTEMS . . . . 153
3.2.1 NOETHER'S THEOREM WITH STRICT INVARIANCE 155
3.2.2 GENERALIZED THEOREM OF NOETHER 156
3.3 LAGRANGIAN DENSITY AND EQUATIONS O F MOTION FOR A FIELD THEORY 157
3.4 LAGRANGIAN DENSITY FOR MAXWELL FIELDS WITH SOURCES 163
3.5 SYMMETRIES AND NOETHER INVARIANTS 168
3.5.1 INVARIANCE UNDER ONE-PARAMETER GROUPS 169
3.5.2 GAUGE TRANSFORMATIONS AND LAGRANGIAN DENSITY . . . . 171
3.5.3 INVARIANCE UNDER TRANSLATIONS 175
3.5.4 INTERPRETATION OF THE CONSERVATION LAWS 179
3.6 WAVE EQUATION AND GREEN FUNCTIONS 183
3.6.1 SOLUTIONS IN NONCOVARIANT FORM 183
3.6.2 SOLUTIONS OF THE WAVE EQUATION IN COVARIANT FORM . . . 188
IMAGE 3
CONTENTS XI
3.7 RADIATION O F AN ACCELERATED CHARGE 193
4 SIMPLE APPLICATIONS O F MAXWELL THEORY 1 99
4.1 INTRODUCTION 199
4.2 PLANE WAVES IN A VACUUM AND IN HOMOGENEOUS INSULATING MEDIA 199
4.2.1 DISPERSION RELATION AND HARMONIC SOLUTIONS 199
4.2.2 COMPLETELY POLARIZED ELECTROMAGNETIC WAVES 205
4.2.3 DESCRIPTION O F POLARIZATION 209
4.3 SIMPLE RADIATING SOURCES 213
4.3.1 TYPICAL DIMENSIONS O F RADIATING SOURCES 214
4.3.2 DESCRIPTION BY MEANS O F MULTIPOLE RADIATION 216
4.3.3 THE HERTZIAN DIPOLE 220
4.4 REFRACTION O F HARMONIC WAVES 225
4.4.1 INDEX OF REFRACTION AND ANGULAR RELATIONS 225
4.4.2 DYNAMICS O F REFRACTION AND REFLECTION 227
4.5 GEOMETRIC OPTICS, LENSES AND NEGATIVE INDEX O F REFRACTION . . 232
4.5.1 OPTICAL SIGNALS IN COORDINATE AND IN MOMENTUM SPACE . 232 4.5.2
GEOMETRIC (RAY) OPTICS AND THIN LENSES 236
4.5.3 MEDIA WITH NEGATIVE INDEX OF REFRACTION 240
4.5.4 METAMATERIALS WITH NEGATIVE INDEX OF REFRACTION . . . . 247 4.6
THE APPROXIMATION O F PARAXIAL BEAMS 249
4.6.1 HELMHOLTZ EQUATION IN PARAXIAL APPROXIMATION . . . . 249
4.6.2 THE GAUSSIAN SOLUTION 250
4.6.3 ANALYSIS OF THE GAUSSIAN SOLUTION 252
4.6.4 FURTHER PROPERTIES OF THE GAUSSIAN BEAM 256
5 LOCAL GAUGE THEORIES 26 1
5.1 INTRODUCTION 261
5.2 KLEIN-GORDON EQUATION AND MASSIVE PHOTONS 261
5.3 THE BUILDING BLOCKS OF MAXWELL THEORY 265
5.4 NON-ABELIAN GAUGE THEORIES 269
5.4.1 THE STRUCTURE GROUP AND ITS LIE ALGEBRA 269
5.4.2 GLOBALLY INVARIANT LAGRANGE DENSITIES 276
5.4.3 THE GAUGE GROUP 277
5.4.4" POTENTIAL AND COVARIANT DERIVATIVE 278
5.4.5 FIELD STRENGTH TENSOR AND CURVATURE 282
5.4.6 GAUGE-INVARIANT LAGRANGE DENSITIES 284
5.4.7 PHYSICAL INTERPRETATION 288
5.4.8 *MORE ON THE GAUGE GROUP 290
5.5 THE U(2) THEORY OF ELECTROWEAK INTERACTIONS 295
5.5.1 A U(2) GAUGE THEORY WITH MASSLESS GAUGE FIELDS . . . 295 5.5.2
SPONTANEOUS SYMMETRY BREAKING 297
5.5.3 APPLICATION TO THE U(2) THEORY 303
IMAGE 4
XII
CONTENTS
5.6 EPILOGUE AND PERSPECTIVES 307
6 CLASSICAL FIELD THEORY O F GRAVITATION 309
6.1 INTRODUCTION 309
6.2 PHENOMENOLOGY O F GRAVITATIONAL INTERACTIONS 310
6.2.1 PARAMETERS AND ORDERS OF MAGNITUDE 310
6.2.2 EQUIVALENCE PRINCIPLE AND UNIVERSALITY 312
6.2.3 RED SHIFT AND OTHER EFFECTS O F GRAVITATION 316
6.2.4 SOME CONJECTURES AND FURTHER PROGRAM 322
6.3 MATTER AND NONGRAVITATIONAL FIELDS 322
6.4 SPACETIMES AS SMOOTH MANIFOLDS 325
6.4.1 MANIFOLDS, CURVES, AND VECTOR FIELDS 325
6.4.2 ONE-FORMS, TENSORS, AND TENSOR FIELDS 332
6.4.3 COORDINATE EXPRESSIONS AND TENSOR CALCULUS 335
6.5 PARALLEL TRANSPORT AND CONNECTION 343
6.5.1 METRIC, SCALAR PRODUCT, AND INDEX 343
6.5.2 CONNECTION AND COVARIANT DERIVATIVE 345
6.5.3 TORSION AND CURVATURE TENSOR FIELDS 349
6.5.4 THE LEVI-CIVITA CONNECTION 351
6.5.5 PROPERTIES OF THE LEVI-CIVITA CONNECTION 353
6.5.6 GEODESIES ON SEMI-RIEMANNIAN SPACETIMES 356
6.5.7 MORE PROPERTIES OF THE CURVATURE TENSOR 360
6.6 THE EINSTEIN EQUATIONS 363
6.6.1 ENERGY-MOMENTUM TENSOR FIELD IN CURVED SPACETIME 363 6.6.2 RICCI
TENSOR, SCALAR CURVATURE, AND EINSTEIN TENSOR . . 364 6.6.3 THE BASIC
EQUATIONS 366
6.7 GRAVITATIONAL FIELD OF A SPHERICALLY SYMMETRIC MASS DISTRIBUTION 371
6.7.1 THE SCHWARZSCHILD METRIC 372
6.7.2 TWO OBSERVABLE EFFECTS 374
6.7.3 THE SCHWARZSCHILD RADIUS IS AN EVENT HORIZON . . . . 382
6.8 SOME CONCLUDING REMARKS 385
BIBLIOGRAPHY 387
SOME HISTORICAL REMARKS 389
EXERCISES 395
SELECTED SOLUTIONS OF THE EXERCISES 403
INDEX 429
ABOUT THE AUTHOR 433 |
| any_adam_object | 1 |
| author | Scheck, Florian 1936-2024 |
| author_GND | (DE-588)121611493 |
| author_facet | Scheck, Florian 1936-2024 |
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| dewey-full | 530.14 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14 |
| dewey-search | 530.14 |
| dewey-sort | 3530.14 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| institution | BVB |
| isbn | 9783642279843 9783642279850 |
| language | English |
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| physical | XII, 433 S. graph. Darst. |
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| spelling | Scheck, Florian 1936-2024 Verfasser (DE-588)121611493 aut Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation Florian Scheck Berlin [u.a.] Springer 2012 XII, 433 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Feldtheorie (DE-588)4016698-3 gnd rswk-swf Feldtheorie (DE-588)4016698-3 s DE-604 Erscheint auch als Online-Ausgabe Classical field theory X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3944530&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025119547&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scheck, Florian 1936-2024 Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4016698-3 |
| title | Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation |
| title_auth | Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation |
| title_exact_search | Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation |
| title_full | Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation Florian Scheck |
| title_fullStr | Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation Florian Scheck |
| title_full_unstemmed | Classical field theory on electrodynamics, non-Abelian gauge theories, and gravitation Florian Scheck |
| title_short | Classical field theory |
| title_sort | classical field theory on electrodynamics non abelian gauge theories and gravitation |
| title_sub | on electrodynamics, non-Abelian gauge theories, and gravitation |
| topic | Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Feldtheorie |
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