Geometrical physics in Minkowski spacetime
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| Format: | Buch |
| Sprache: | English |
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London [u.a.]
Springer
2001
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| Schriftenreihe: | Springer monographs in mathematics
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| 100 | 1 | |a Rowe, E. G. Peter |d 1938-1998 |e Verfasser |0 (DE-588)122663616 |4 aut | |
| 245 | 1 | 0 | |a Geometrical physics in Minkowski spacetime |c E. G. Peter Rowe |
| 264 | 1 | |a London [u.a.] |b Springer |c 2001 | |
| 300 | |a XV, 248 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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| DE-BY-UBR_katkey | 3145844 |
| DE-BY-UBR_location | 80 |
| DE-BY-UBR_media_number | 069030186336 |
| _version_ | 1822698893601669120 |
| adam_text | E.G. PETER ROWE GEOMETRICAL PHYSICS IN MINKOWSKI SPACETIME WITH 112
FIGURES SPRINGER CONTENTS 1. SPACETIME 1 1.1 SPACETIME IS A
FOUR-DIMENSIONAL CONTINUUM 3 1.2 ARISTOTELIAN SPACETIME
(PRE-RELATIVISTIC) 4 1.3 GALILEAN SPACETIME 5 1.4 PRINCIPLES OF SPECIAL
RELATIVITY 7 1.5 MINKOWSKIAN INERTIAL FRAMES OF REFERENCE 8 1.6 POINCARE
TRANSFORMATIONS 12 1.6.1 STRAIGHT LINES 14 1.6.2 LIGHT RAYS 16 1.6.3
UNITS 20 1.6.4 ORIENTATIONS AND DEFINITION OF LORENTZ TRANSFORMATIONS 22
1.6.5 INVERSE LORENTZ TRANSFORMATIONS 22 1.7 INERTIAL COORDINATES IN
SPACETIME 24 1.7.1 ABSOLUTE VS RELATIVE DIAGRAMS 24 1.7.2 THE USE OF
INERTIAL COORDINATES 26 1.7.3 RELATION OF COORDINATES FOR BOOSTED FRAMES
26 1.8 GEOMETRICAL RELATIONS BETWEEN EVENTS 28 1.8.1 SPACETIME INTERVAL
28 1.8.2 INVARIANT RELATIONS 29 1.9 POINCARE GROUP 31 1.9.1 SUBGROUP OF
TRANSLATIONS 31 1.9.2 ROTATION SUBGROUP 32 1.9.3 BOOSTS DO NOT FORM A
SUBGROUP 33 1.10 PHYSICAL SPACETIME DIAGRAMS 34 1.11 PROBLEMS 36
REFERENCES 41 2. VECTORS IN SPACETIME 43 2.1 TRANSLATION VECTORS IN
SPACETIME 44 2.1.1 VECTOR SPACE 45 2.1.2 ADDITION 46 2.1.3
MULTIPLICATION BY A SCALAR 47 2.1.4 INERTIAL BASIS VECTORS 48 2.1.5
DECOMPOSITION 49 XII CONTENTS 2.1.6 TRANSFORMATION OF BASIS VECTORS 49
2.2 SCALAR PRODUCT OF SPACETIME VECTORS 51 2.3 CLASSIFICATION OF VECTORS
53 2.3.1 FUTURE-POINTING LIGHTLIKE VECTORS 54 2.3.2 PAST-POINTING
LIGHTLIKE VECTORS 54 2.3.3 FUTURE-POINTING TIMELIKE VECTORS 55 2.3.4
PAST-POINTING TIMELIKE VECTORS 55 2.3.5 SPACELIKE VECTORS 55 2.3.6 ZERO
VECTOR 56 2.4 THE FAMOUS KINEMATICAL EFFECTS 56 2.4.1 TIME DILATION 57
2.4.2 THE TWIN PARADOX 59 2.4.3 LENGTH CONTRACTION 62 2.4.4 ADDITION OF
VELOCITIES 63 2.4.5 TWO MOON ROCKETS 65 2.4.6 THE PROBLEM OF CRASHING
MIRRORS 66 2.5 THE GENERALISED VECTOR SPACE V 67 2.6 PROPER TIME AND
CONCEPTS OF VELOCITY 68 2.6.1 SPACETIME VELOCITY 69 2.6.2 PROPER TIME 71
2.6.3 RELATIVE VELOCITY WITH RESPECT TO AN INERTIAL FRAME... 72 2.6.4
GENERAL ADDITION OF VELOCITIES FORMULA 74 2.6.5 ACCELERATION 75 2.7
LIGHT RAYS 76 2.7.1 LIGHTLIKE VECTORS 76 2.7.2 HARMONIC LIGHT 81 2.7.3
SCALAR FIELD THEORY FOR LIGHT 83 2.8 DESCRIPTION OF UNIFORMLY MOVING
OBJECTS 85 2.8.1 EXAMPLE: ROD LYING IN THE DIRECTION OF MOTION 87 2.8.2
EXAMPLE: ROD AT AN ANGLE TO THE DIRECTION OF MOTION. 88 2.8.3 EXAMPLE:
PARALLELOGRAM AT REST IN K 88 2.8.4 EXAMPLE: PARALLELEPIPED AT REST IN K
89 2.8.5 EXAMPLE: A UNIFORMLY MOVING ROD CAN APPEAR TO DIP 89 2.9
PROBLEMS 90 REFERENCES 98 3. ASYMPTOTIC MOMENTUM CONSERVATION 99 3.1
PARTICLE MOMENTA 99 3.1.1 MASSIVE PARTICLES 100 3.1.2 MASSLESS PARTICLES
102 3.1.3 ENERGY AND THREE-MOMENTUM OF ONE PARTICLE WITH RESPECT TO THE
REST FRAME OF ANOTHER PARTICLE 104 3.2 CONSERVATION OF ASYMPTOTIC
MOMENTUM 104 3.3 THREE-PARTICLE PROCESSES 106 3.4 A KINEMATICAL FUNCTION
108 CONTENTS XIII 3.5 COMPTON EFFECT 109 3.6 CENTRE-OF-MOMENTUM FRAME
110 3.6.1 TWO-PARTICLE CM-FRAME 112 3.7 THRESHOLD ENERGY FOR PARTICLE
PRODUCTION 113 3.8 SCATTERING FORMULAE 115 3.8.1 LABORATORY FRAME 116
3.8.2 CM-FRAME 116 3.9 PROBLEMS 119 REFERENCES 124 4. COVECTORS AND
DYADICS IN SPACETIME 125 4.1 COVECTORS IN SPACETIME 126 4.1.1 COMPONENTS
OF A COVECTOR 126 4.1.2 TRANSFORMATION LAW FOR COMPONENTS 126 4.1.3 THE
DUAL SPACE (OR COSPACE) 127 4.1.4 COBASES AND THEIR TRANSFORMATION LAW
127 4.1.5 THE NATURAL ISOMORPHISM BETWEEN V AND V* 128 4.1.6 GEOMETRICAL
INTERPRETATION 128 4.2 GRADIENT OF A SCALAR FIELD 130 4.2.1
APPROXIMATION OF SCALAR FIELDS AND THE COVECTOR GRA- DIENT 130 4.2.2
COMPONENTS OF THE COVECTOR GRADIENT 131 4.2.3 VECTOR GRADIENT 132 4.2.4
GRADIENT OPERATORS 133 4.2.5 COBASIS AS THE COVECTOR GRADIENT OF THE
INERTIAL COORDINATES 133 4.3 DYADICS IN SPACETIME 133 4.3.1 LINEAR
TRANSFORMATIONS AS DYADICS 134 4.3.2 SIMPLEST PROPERTIES 135 4.3.3 BASES
FOR THE SPACE OF DYADICS 135 4.3.4 A UNIT DYADIC: THE CONTRAVARIANT
METRIC 136 4.3.5 A GEOMETRICAL EXAMPLE: REFLECTION DYADICS 137 4.3.6
TRANSFORMATION LAW FOR COMPONENTS 137 4.3.7 TRANSPOSED DYADICS AND
SYMMETRIES 138 4.3.8 SCALAR PRODUCTS 139 4.3.9 TRACE 139 4.4 ROTATION
AND BOOST DYADICS 140 4.5 GRADIENT OF A VECTOR FIELD 141 4.6 EXTENSIONS
143 4.7 DUAL OF AN ANTISYMMETRIC DYADIC 144 4.7.1 THE DEFINITION IS
BASIS-INDEPENDENT 145 4.7.2 EXPLICIT COMPONENTS OF THE DUAL 146 4.7.3 AN
ANTISYMMETRIC BASIS 147 4.7.4 ANGULAR MOMENTUM DYADIC FOR A FREELY
MOVING PARTICLE 148 XIV CONTENTS 4.8 CONCEPT OF VOLUME IN SPACETIME 149
4.8.1 DIMENSION TWO 149 4.8.2 UNORIENTED REGION 149 4.8.3 ORIENTED
REGION 150 4.8.4 DIMENSIONS THREE AND FOUR 151 4.8.5 THE COMMON MEASURE
IN MINKOWSKI SPACETIME 152 4.8.6 CHANGE OF VARIABLES FORMULA 153 4.9
DIVERGENCE THEOREM IN SPACETIME 154 4.9.1 INTEGRAL FORM OF THE
CONSERVATION LAW 154 4.9.2 DIVERGENCE THEOREM IN SPACETIME: GEOMETRICAL
EXPRESSION 156 4.9.3 DIVERGENCE THEOREM: ANALYTICAL EXPRESSION 157 4.10
PROBLEMS 158 REFERENCES 164 5. ELECTROMAGNETISM 165 5.1 MAXWELL S
EQUATIONS 165 5.1.1 VERIFICATION OF MAXWELL S EQUATIONS 167 5.2
TRANSFORMATION OF ELECTRIC AND MAGNETIC FIELDS 168 5.3 EXAMPLE: AN
INFINITE LINE OF CHARGE 169 5.3.1 FIELDS AND SOURCES WITH RESPECT TO THE
REST FRAME K 170 5.3.2 FIELDS AND SOURCES WITH RESPECT TO K 171 5.4
VECTOR POTENTIAL 172 5.4.1 ALTERNATIVE FORM FOR THE HOMOGENEOUS MAXWELL
EQUATION 173 5.4.2 AN EXPLICIT VECTOR POTENTIAL 173 5.4.3 LORENTZ
CONDITION 174 5.5 ELECTRIC CURRENT DENSITY 174 5.5.1 CHARGED DUST 175
5.5.2 DENSITY OF CHARGE 176 5.5.3 FLUX OF CHARGE 177 5.5.4 CONSERVATION
OF CHARGE 178 5.5.5 CONSERVATION OF CHARGE ALONG A WORLDLINE 180 5.6
POINT PARTICLE: A SINGULAR SOURCE 180 5.6.1 THE INTRINSIC VARIABLES 182
5.6.2 ELECTROMAGNETIC FIELD FOR A POINT CHARGE 185 5.6.3 ELECTRIC AND
MAGNETIC FIELDS IN THE RETARDED REST FRAME 186 5.6.4 ELECTRIC AND
MAGNETIC FIELDS IN THE LABORATORY 186 5.6.5 MAXWELL S EQUATIONS FOR A
POINT CHARGE 187 5.6.6 THE REGION OFF THE WORLDLINE: EMPTY SPACE 188
5.6.7 THE ELECTROMAGNETIC FIELD AS A DISTRIBUTION 188 5.6.8 CHANGE OF
VARIABLES IN SPACETIME INTEGRALS 189 5.6.9 MAXWELL S EQUATIONS ALONG THE
WORLDLINE 190 5.7 PLANE WAVES 191 CONTENTS XV 5.7.1 PLANE POLARISED
WAVES 192 5.7.2 CIRCULARLY POLARISED WAVES 193 5.7.3 CHANGE OF BASIS: A
BOOST IN THE DIRECTION OF PROPAGATION 193 5.7.4 CHANGE TO A GENERAL
MOVING FRAME 194 5.8 PROBLEMS 195 REFERENCES 200 6. THE ENERGY TENSOR
201 6.1 THE ENERGY TENSOR FOR DUST 202 6.2 THE ENERGY TENSOR IN GENERAL
203 6.2.1 CONSERVATION OF FOUR-MOMENTUM 204 6.3 THE VARIATIONAL
PRINCIPLE 206 6.3.1 ACTION FOR THE ELECTROMAGNETIC FIELD 208 6.3.2
ACTION FOR A CHARGED PARTICLE IN AN EXTERNAL FIELD 209 6.3.3 ACTION FOR
CHARGED PARTICLES INTERACTING ELECTROMAG- NETICALLY 210 6.4 NONINERTIAL
COORDINATES 211 6.4.1 NEW BASIS VECTORS 211 6.4.2 NEW COMPONENTS 212 6.5
CONSTRUCTION OF THE ENERGY TENSOR 213 6.5.1 FIRST EXAMPLE: ENERGY TENSOR
FOR THE FREE SCALAR FIELD 218 6.5.2 THE TOTAL ENERGY TENSOR HAS ZERO
DIVERGENCE 219 6.5.3 SECOND EXAMPLE: ENERGY TENSOR FOR THE ELECTROMAG-
NETIC FIELD 219 6.5.4 THIRD EXAMPLE: ENERGY TENSOR FOR A POINT PARTICLE
... 220 6.6 ENERGY IN THE ELECTROMAGNETIC FIELD 221 6.6.1 FOUR-MOMENTUM
IN A PLANE WAVE 222 6.6.2 RADIATION FROM AN ACCELERATING POINT CHARGE
223 6.7 EQUATIONS OF MOTION FOR CHARGED DUST 224 6.7.1 UNCHARGED
INCOHERENT DUST 224 6.7.2 CHARGED DUST 226 6.7.3 FRAME-DEPENDENT
EQUATION OF MOTION FOR CHARGED DUST227 6.8 PERFECT FLUID 228 6.8.1
EQUATIONS OF MOTION 229 6.8.2 FIRST LAW OF THERMODYNAMICS 229 6.8.3
LABEL SPACE 230 6.8.4 LAGRANGIAN FOR A PERFECT FLUID 232 6.9 PROBLEMS
235 REFERENCES 239 INDEX 241
|
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| author | Rowe, E. G. Peter 1938-1998 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV013380499 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:26:38Z |
| institution | BVB |
| isbn | 1852333669 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009127153 |
| oclc_num | 247888694 |
| open_access_boolean | |
| owner | DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-11 DE-83 |
| owner_facet | DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-11 DE-83 |
| physical | XV, 248 S. graph. Darst. : 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spellingShingle | Rowe, E. G. Peter 1938-1998 Geometrical physics in Minkowski spacetime Special relativity (Physics) Minkowski-Raum (DE-588)4293944-6 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| subject_GND | (DE-588)4293944-6 (DE-588)4182215-8 |
| title | Geometrical physics in Minkowski spacetime |
| title_auth | Geometrical physics in Minkowski spacetime |
| title_exact_search | Geometrical physics in Minkowski spacetime |
| title_full | Geometrical physics in Minkowski spacetime E. G. Peter Rowe |
| title_fullStr | Geometrical physics in Minkowski spacetime E. G. Peter Rowe |
| title_full_unstemmed | Geometrical physics in Minkowski spacetime E. G. Peter Rowe |
| title_short | Geometrical physics in Minkowski spacetime |
| title_sort | geometrical physics in minkowski spacetime |
| topic | Special relativity (Physics) Minkowski-Raum (DE-588)4293944-6 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| topic_facet | Special relativity (Physics) Minkowski-Raum Spezielle Relativitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009127153&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT roweegpeter geometricalphysicsinminkowskispacetime |