Foundations of classical electrodynamics: charge, flux, and metric
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2003
|
| Schriftenreihe: | Progress in mathematical physics
33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 410 S. |
| ISBN: | 9780817642228 3764342226 |
Internformat
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| 245 | 1 | 0 | |a Foundations of classical electrodynamics |b charge, flux, and metric |c Friedrich W. Hehl ; Yuri N. Obukhov |
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Datensatz im Suchindex
| _version_ | 1804130033897308160 |
|---|---|
| adam_text | FRIEDRICH W. HEHL YURI N. OBUKHOV FOUNDATIONS OF CLASSICAL
ELECTRODYNAMICS CHARGE, FLUX, AND METRIC BIRKHAUSER BOSTON * BASEL *
BERLIN CONTENTS PREFACE V INTRODUCTION 1 FIVE PLUS ONE AXIOMS 1
TOPOLOGICAL APPROACH 3 ELECTROMAGNETIC SPACETIME RELATION AS FIFTH AXIOM
4 ELECTRODYNAMICS IN MATTER AND THE SIXTH AXIOM 5 LIST OF AXIOMS 5 A
REMINDER: ELECTRODYNAMICS IN 3-DIMENSIONAL EUCLIDEAN VECTOR CALCULUS 5
ON THE LITERATURE 7 REFERENCES 11 A MATHEMATICS: SOME EXTERIOJ* CALCULUS
17 WHY EXTERIOR DIFFERENTIAL FORMS? 19 A.I ALGEBRA 23 A.I.I A REAL
VECTOR SPACE AND ITS DUAL 23 A.1.2 TENSORS OF TYPE [J] 25 A. 1.3 A
GENERALIZATION OF TENSORS: GEOMETRIC QUANTITIES 27 A.1.4 ALMOST COMPLEX
STRUCTURE 29 A.I.5 EXTERIOR P-FORMS 29 X CONTENTS A.1.6 EXTERIOR
MULTIPLICATION 30 A. 1.7 INTERIOR MULTIPLICATION OF A VECTOR WITH A FORM
33 A. 1.8 VOLUME ELEMENTS ON A VECTOR SPACE, DENSITIES, ORIENTATION ...
34 A. 1.9 LEVI-CIVITA SYMBOLS AND GENERALIZED KRONECKER DELTAS 36 A.
1.10 THE SPACE M 6 OF TWO-FORMS IN FOUR DIMENSIONS 40 A.I.11 ALMOST
COMPLEX STRUCTURE ON M 6 43 A.I.12 COMPUTER ALGEBRA 45 A.2 EXTERIOR
CALCULUS 57 A.2.1 DIFFERENTIABLE MANIFOLDS 57 A.2.2 VECTOR FIELDS 61
A.2.3 ONE-FORM FIELDS, DIFFERENTIAL P-FORMS 62 A.2.4 PICTURES OF VECTORS
AND ONE-FORMS 63 A.2.5 VOLUME FORMS AND ORIENTABILITY 64 A.2.6 TWISTED
FORMS 66 A.2.7 EXTERIOR DERIVATIVE 67 A.2.8 FRAME AND COFRAME 70 A.2.9
MAPS OF MANIFOLDS: PUSH-FORWARD AND PULL-BACK 71 A.2.10 LIE DERIVATIVE
73 A.2.11 EXCALC, A REDUCE PACKAGE 78 A.2.12 CLOSED AND EXACT FORMS, DE
RHAM COHOMOLOGY GROUPS . . . . 83 A.3 INTEGRATION ON A MANIFOLD 87 A.3.1
INTEGRATION OF 0-FORMS AND ORIENTABILITY OF A MANIFOLD 87 A.3.2
INTEGRATION OF N-FORMS 88 A.3.3 INTEGRATION OF P-FORMS WITH 0 P N
89 A.3.4 STOKES THEOREM 93 A.3.5 DE RHAM S THEOREMS 96 REFERENCES 103
B AXIOMS OF CLASSICAL ELECTRODYNAMICS 107 B.I ELECTRIC CHARGE
CONSERVATION 109 B.I.I COUNTING CHARGES. ABSOLUTE AND RELATIVE DIMENSION
109 B.1.2 SPACETIME AND THE FIRST AXIOM 114 B.I.3 ELECTROMAGNETIC
EXCITATION H 116 B.I.4 TIME-SPACE DECOMPOSITION OF THE INHOMOGENEOUS
MAXWELL EQUATION 117 B.2 LORENTZ FORCE DENSITY 121 B.2.1 ELECTROMAGNETIC
FIELD STRENGTH F * 121 B.2.2 SECOND AXIOM RELATING MECHANICS AND
ELECTRODYNAMICS 123 B.2.3 THE FIRST THREE INVARIANTS OF THE
ELECTROMAGNETIC FIELD 126 CONTENTS XI B.3 MAGNETIC FLUX CONSERVATION 129
B.3.1 THIRD AXIOM 129 B.3.2 ELECTROMAGNETIC POTENTIAL 132 B.3.3
ABELIAN CHERN-SIMONS AND KIEHN 3-FORMS 134 B.3.4 MEASURING THE
EXCITATION 136 B.4 BASIC CLASSICAL ELECTRODYNAMICS SUMMARIZED, EXAMPLE
143 B.4.1 INTEGRAL VERSION AND MAXWELL S EQUATIONS 143 B.4.2 LENZ AND
ANTI-LENZ RULE 146 B.4.3 JUMP CONDITIONS FOR ELECTROMAGNETIC
EXCITATION AND FIELD STRENGTH 150 B.4.4 ARBITRARY LOCAL NONINERTIAL
FRAME: MAXWELL S EQUATIONS IN COMPONENTS 151 B.4.5 ^ELECTRODYNAMICS IN
FLATLAND: 2DEG AND QHE 152 B.5 ELECTROMAGNETIC ENERGY-MOMENTUM CURRENT
AND ACTION 163 B.5.1 FOURTH AXIOM: LOCALIZATION OF ENERGY-MOMENTUM 163
B.5.2 ENERGY-MOMENTUM CURRENT, ELECTRIC/MAGNETIC RECIPROCITY . . . 166
B.5.3 TIME-SPACE DECOMPOSITION OF THE ENERGY-MOMENTUM AND THE LENZ RULE
174 B.5.4 ACTION 177 B.5.5 COUPLING OF THE ENERGY-MOMENTUM CURRENT TO
THE COFRAME . . 180 B.5.6 MAXWELL S EQUATIONS AND THE ENERGY-MOMENTUM
CURRENT IN EXCALC 184 REFERENCES 187 C MORE MATHEMATICS 193 C.I LINEAR
CONNECTION 195 C.I.I COVARIANT DIFFERENTIATION OF TENSOR FIELDS 195
C.1.2 LINEAR CONNECTION 1-FORMS 197 C.1.3 COVARIANT DIFFERENTIATION OF
A GENERAL GEOMETRIC QUANTITY . . . 199 C.1.4 PARALLEL TRANSPORT 200
C.1.5 TORSION AND CURVATURE .....* 201 C.1.6 CARTAN S GEOMETRIC
INTERPRETATION OF TORSION AND CURVATURE . .205 C.I.7 COVARIANT EXTERIOR
DERIVATIVE 207 C.1.8 THE FORMS O(A), CONNL(A,B), TORSION2(A),
CURV2(A,B) 208 C.2 METRIC 211 C.2.1 METRIC VECTOR SPACES 212 C.2.2
ORTHONORMAL, HALF-NULL 1 , AND NULL FRAMES, THE COFRAME STATEMENT 213
C.2.3 METRIC VOLUME 4-FORM 216 XII CONTENTS C.2.4 DUALITY OPERATOR FOR
2-FORMS AS A SYMMETRIC ALMOST COMPLEX STRUCTURE ON M 6 218 C.2.5 FROM
THE DUALITY OPERATOR TO A TRIPLET OF COMPLEX 2-FORMS . . . 220 C.2.6
PROM THE TRIPLET OF COMPLEX 2-FORMS TO A DUALITY OPERATOR . . . 222
C.2.7 PROM A TRIPLET OF COMPLEX 2-FORMS TO THE METRIC:
SCHONBERG-URBANTKE FORMULAS 224 C.2.8 HODGE STAR AND EXCALC S # 225
C.2.9 MANIFOLD WITH A METRIC, LEVI-CIVITA CONNECTION 228 C.2.10
CODIFFERENTIAL AND WAVE OPERATOR, ALSO IN EXCALC 230 C.2.11
NONMETRICITY 231 C.2.12 POST-RIEMANNIAN PIECES OF THE CONNECTION 233
C.2.13 EXCALC AGAIN 236 REFERENCES 241 D THE MAXWELL-LORENTZ SPACETIME
RELATION 243 D.I A LINEAR RELATION BETWEEN H AND F 245 D.I.I THE
CONSTITUTIVE TENSOR OF SPACETIME 245 D.I.2 DECOMPOSING THE CONSTITUTIVE
TENSOR 248 D.I.3 DECOMPOSING ENERGY-MOMENTUM AND ACTION 250 D.1.4
ABELIAN AXION FIELD A 252 D.I.5 SKEWON FIELD & J AND DISSIPATION 253
D.I.6 PRINCIPAL PART OF THE CONSTITUTIVE TENSOR 258 D.I.7
SIX-DIMENSIONAL REPRESENTATION OF THE SPACETIME RELATION . . . . 258
D.I.8 SPECIAL CASE: SPATIALLY ISOTROPIC SKEWON FIELD 261 D.2
PROPAGATION OF ELECTROMAGNETIC WAVES: QUARTIC WAVE SURFACE 263 D.2.1
FRESNEL EQUATION 263 D.2.2 PROPERTIES OF THE TAMM-RUBILAR TENSOR
DENSITY 267 D.2.3 PRESNEL EQUATION DECOMPOSED INTO TIME AND SPACE . . .
. . . . 270 D.3 FIRST CONSTRAINT: ELECTRIC/MAGNETIC RECIPROCITY 273
D.3.1 RECIPROCITY IMPLIES CLOSURE 273 D.3.2 ALMOST COMPLEX STRUCTURE AND
DILATON FIELD 274 D.3.3 DRAW THE SQUARE ROOT OF THE 6D NEGATIVE UNIT
MATRIX 275 D.4 SECOND CONSTRAINT: VANISHING SKEWON FIELD. EMERGENCE OF
THE LIGHT CONE 279 D.4.1 LAGRANGIAN AND SYMMETRY 279 D.4.2 DUALITY
OPERATOR : 280 D.4.3 ALGEBRAIC SOLUTION OF THE CLOSURE AND SYMMETRY
RELATIONS .... 281 D.4.4 PROM A QUARTIC WAVE SURFACE TO THE LIGHT CONE
286 CONTENTS XIII D.5 EXTRACTING THE METRIC BY AN ALTERNATIVE METHOD 291
D.5.1 TRIPLET OF SELF-DUAL 2-FORMS AND METRIC 291 D.5.2 MAXWELL-LORENTZ
SPACETIME RELATION AND MINKOWSKI SPACETIME . 294 D.5.3 HODGE STAR
OPERATOR AND ISOTROPY 295 D.5.4 COVARIANCE PROPERTIES 296 D.6 FIFTH
AXIOM: MAXWELL-LORENTZ SPACETIME RELATION 301 D.6.1 THE AXIOM 301 D.6.2
ON THE POINCARE AND THE LORENTZ GROUPS 303 D.6.3 EXTENSIONS. DISSOLVING
LORENTZ INVARIANCE? 304 REFERENCES 307 E ELECTRODYNAMICS IN VACUUM AND
IN MATTER 313 E.I STANDARD MAXWELL-LORENTZ THEORY IN VACUUM 315 E.I.I
MAXWELL-LORENTZ EQUATIONS, IMPEDANCE OF THE VACUUM 315 E.1.2 ACTION 317
E.I.3 FOLIATION OF A SPACETIME CARRYING A METRIC. EFFECTIVE PERMEABIL-
ITIES 317 E.1.4 ELECTROMAGNETIC ENERGY AND MOMENTUM 319 E.2
ELECTROMAGNETIC SPACETIME RELATIONS BEYOND LOCALITY AND LINEARITY 323
E.2.1 KEEPING THE FIRST FOUR AXIOMS FIXED 323 E.2.2 MASHHOON 324 E.2.3
HEISENBERG-EULER 325 E.2.4 BORN-INFELD 326 E.2.5 PLEBANSKI 327 E.3
ELECTRODYNAMICS IN MATTER, CONSTITUTIVE LAW 329 E.3.1 SPLITTING OF THE
CURRENT: SIXTH AXIOM 329 E.3.2 MAXWELL S EQUATIONS IN MATTER 331 E.3.3
ENERGY-MOMENTUM CURRENTS IN MATTER 332 E.3.4 LINEAR CONSTITUTIVE LAW 337
E.3.5 EXPERIMENT OF WALKER & WALKED 339 E.3.6 EXPERIMENT OF JAMES 342
E.4 ELECTRODYNAMICS OF MOVING CONTINUA 347 E.4.1 LABORATORY AND MATERIAL
FOLIATION 347 E.4.2 ELECTROMAGNETIC FIELD IN LABORATORY AND MATERIAL
FRAMES . . . . 351 E.4.3 OPTICAL METRIC FROM THE CONSTITUTIVE LAW 354
E.4.4 ELECTROMAGNETIC FIELD GENERATED IN MOVING CONTINUA 355 E.4.5 THE
EXPERIMENTS OF RONTGEN AND WILSON & WILSON 357 E.4.6 NONINERTIAL
ROTATING COORDINATES 361 XIV CONTENTS E.4.7 ROTATING OBSERVER 363
E.4.8 ACCELERATING OBSERVER 364 E.4.9 THE PROPER REFERENCE FRAME OF THE
NONINERTIAL OBSERVER ( NONINERTIAL FRAME ) 366 E.4.10 UNIVERSALITY OF
THE MAXWELL-LORENTZ SPACETIME RELATION . . . .368 REFERENCES 371
OUTLOOK 375 HOW DOES GRAVITY AFFECT ELECTRODYNAMICS? 376
REISSNER-NORDSTROM SOLUTION 377 ROTATING SOURCE: KERR-NEWMAN SOLUTION
379 ELECTRODYNAMICS OUTSIDE BLACK HOLES AND NEUTRON STARS 381 FORCE-FREE
ELECTRODYNAMICS 383 REMARKS ON TOPOLOGY AND ELECTRODYNAMICS 385
SUPERCONDUCTIVITY: REMARKS ON GINZBURG-LANDAU THEORY 387 CLASSICAL
(FIRST QUANTIZED) DIRAC FIELD 388 ON THE QUANTUM HALL EFFECT AND THE
COMPOSITE FERMION 390 ON QUANTUM ELECTRODYNAMICS 390 ON ELECTROWEAK
UNIFICATION 391 REFERENCES 393 AUTHOR INDEX 397 SUBJECT INDEX 403
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:14:36Z |
| institution | BVB |
| isbn | 9780817642228 3764342226 |
| language | English |
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| physical | XIV, 410 S. |
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| series | Progress in mathematical physics |
| series2 | Progress in mathematical physics |
| spelling | Hehl, Friedrich W. 1937- Verfasser (DE-588)120517485 aut Foundations of classical electrodynamics charge, flux, and metric Friedrich W. Hehl ; Yuri N. Obukhov Boston [u.a.] Birkhäuser 2003 XIV, 410 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematical physics 33 Elektrodinamik - Matematik Elektrodynamica gtt Eletrodinâmica larpcal Mathematik Electrodynamics Mathematics Elektrodynamik (DE-588)4014251-6 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Elektrodynamik (DE-588)4014251-6 s Mathematische Physik (DE-588)4037952-8 s DE-604 Obuchov, Jurij N. Verfasser aut Progress in mathematical physics 33 (DE-604)BV013823265 33 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010351947&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hehl, Friedrich W. 1937- Obuchov, Jurij N. Foundations of classical electrodynamics charge, flux, and metric Progress in mathematical physics Elektrodinamik - Matematik Elektrodynamica gtt Eletrodinâmica larpcal Mathematik Electrodynamics Mathematics Elektrodynamik (DE-588)4014251-6 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4014251-6 (DE-588)4037952-8 |
| title | Foundations of classical electrodynamics charge, flux, and metric |
| title_auth | Foundations of classical electrodynamics charge, flux, and metric |
| title_exact_search | Foundations of classical electrodynamics charge, flux, and metric |
| title_full | Foundations of classical electrodynamics charge, flux, and metric Friedrich W. Hehl ; Yuri N. Obukhov |
| title_fullStr | Foundations of classical electrodynamics charge, flux, and metric Friedrich W. Hehl ; Yuri N. Obukhov |
| title_full_unstemmed | Foundations of classical electrodynamics charge, flux, and metric Friedrich W. Hehl ; Yuri N. Obukhov |
| title_short | Foundations of classical electrodynamics |
| title_sort | foundations of classical electrodynamics charge flux and metric |
| title_sub | charge, flux, and metric |
| topic | Elektrodinamik - Matematik Elektrodynamica gtt Eletrodinâmica larpcal Mathematik Electrodynamics Mathematics Elektrodynamik (DE-588)4014251-6 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Elektrodinamik - Matematik Elektrodynamica Eletrodinâmica Mathematik Electrodynamics Mathematics Elektrodynamik Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010351947&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013823265 |
| work_keys_str_mv | AT hehlfriedrichw foundationsofclassicalelectrodynamicschargefluxandmetric AT obuchovjurijn foundationsofclassicalelectrodynamicschargefluxandmetric |