Quaternions, Clifford algebras and relativistic physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Basel ; Boston ; Berlin
Birkhäuser
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 173 - 176 |
| Beschreibung: | XII, 179 S. graph. Darst. 24 cm |
| ISBN: | 9783764377908 3764377909 |
Internformat
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| 100 | 1 | |a Girard, Patrick R. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Quaternions, algèbre de Clifford et physique relativiste |
| 245 | 1 | 0 | |a Quaternions, Clifford algebras and relativistic physics |c Patrick R. Girard |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 2007 | |
| 300 | |a XII, 179 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 173 - 176 | ||
| 650 | 4 | |a Clifford, Algèbres de | |
| 650 | 4 | |a Quaternions | |
| 650 | 4 | |a Clifford algebras | |
| 650 | 4 | |a Quaternions | |
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Datensatz im Suchindex
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| adam_text |
PATRICK R. GIRARD
QUATERNIONS,
FFORD ALGEBRA
S AN
D
SLATIVISTI
C PHYSIC
S
BIRKHAUSER
BASEL BOSTON BERLIN
CONTENTS
INTRODUCTION 1
1 QUATERNIONS 3
1.1 GROUP STRUCTUR
E 3
1.2 FINITE GROUPS OF ORDER N 8 4
1.3 QUATERNION GROUP 7
1.4 QUATERNION ALGEBRA H 8
1.4.1 DEFINITIONS 8
1.4.2 POLAR FORM 11
1.4.3 SQUARE ROOT AND N
T
H
ROOT 11
1.4.4 OTHER FUNCTIONS AND REPRESENTATIONS OF QUATERNIONS 14
1.5 CLASSICAL VECTOR CALCULUS 15
1.5.1 SCALAR PRODUCT AND VECTOR PRODUCT 15
1.5.2 TRIPLE SCALAR AND DOUBLE VECTOR PRODUCTS 16
1.6 EXERCISES 17
2 ROTATION GROUPS
SO(4)
AND
SO(3)
19
2.1 ORTHOGONAL GROUPS 0(4
) AND S0(4
) 19
2.2 ORTHOGONAL GROUPS 0(3
) AND S0(3
) 22
2.3 CRYSTALLOGRAPHIC GROUPS 24
2.3.1 DOUBLE CYCLIC GROUPS
C
N
(ORDER
N = 2N)
24
2.3.2 DOUBLE DIHEDRAL GROUPS
D
N
(N = AN)
24
2.3.3 DOUBLE TETRAHEDRA
L GROUP
(N -
24) 25
2.3.4 DOUBLE OCTAHEDRAL GROUP
(N =
48) 26
2.3.5 DOUBLE ICOSAHEDRAL GROUP
(N =
120) 27
2.4 INFINITESIMAL TRANSFORMATIONS OF SO(4) 28
2.5 SYMMETRIES AND INVARIANTS: KEPLER'S PROBLEM 32
2.6 EXERCISES 34
3 COMPLEX QUATERNIONS 37
3.1 ALGEBRA OF COMPLEX QUATERNIONS H(C) 37
3.2 LORENTZ GROUPS 0(1,3
) AND SO(1,3) 38
3.2.1 METRIC 38
CONTENTS
3.2.2 PLANE SYMMETRY 38
3.2.3 GROUPS 0(1,3
) AND S0(L,3
) 39
3.3 ORTHOCHRONOUS, PROPER LORENTZ GROUP 41
3.3.1 PROPERTIES 41
3.3.2 INFINITESIMAL TRANSFORMATIONS OF SO(1,3) 43
3.4 FOUR-VECTORS AND MULTIVECTORS IN H(C) 44
3.5 RELATIVISTIC KINEMATICS VIA H(C) 47
3.5.1 SPECIAL LORENTZ TRANSFORMATION 47
3.5.2 GENERAL PURE LORENTZ TRANSFORMATION 48
3.5.3 COMPOSITION OF VELOCITIES 48
3.6 MAXWELL'S EQUATIONS 50
3.7 GROUP OF CONFORMAL TRANSFORMATIONS 52
3.8 EXERCISES 54
CLIFFORD ALGEBRA 57
4.1 CLIFFORD ALGEBRA 57
4.1.1 DEFINITIONS 57
4.1.2 CLIFFORD ALGEBRA H
G HI OVER R 58
4.2 MULTIVECTOR CALCULUS WITHIN H H 59
4.2.1 EXTERIOR AND INTERIOR PRODUCTS WITH A VECTOR 59
4.2.2 PRODUCT
S OF TWO MULTIVECTORS 61
4.2.3 GENERAL FORMULAS 62
4.2.4 CLASSICAL VECTOR CALCULUS 64
4.3 MULTIVECTOR GEOMETRY 64
4.3.1 ANALYTIC GEOMETRY 64
4.3.2 ORTHOGONAL PROJECTIONS 66
4.4 DIFFERENTIAL OPERATORS 69
4.4.1 DEFINITIONS 69
4.4.2 INFINITESIMAL ELEMENTS OF CURVES, SURFACES AND HYPERSURFACES 69
4.4.3 GENERAL THEOREMS 71
4.5 EXERCISES 72
SYMMETRY GROUPS 75
5.1 PSEUDO-ORTHOGONAL GROUPS 0(1,3
) AND SO(1,3) 75
5.1.1 METRIC 75
5.1.2 SYMMETRY WITH RESPECT T
O A HYPERPLANE 75
5.1.3 PSEUDO-ORTHOGONAL GROUPS 0(1,3
) AND S0(L
, 3) 77
5.2 PROPER ORTHOCHRONOUS LORENTZ GROUP 78
5.2.1 ROTATION GROUP SO(3) 78
5.2.2 PUR
E LORENTZ TRANSFORMATION 79
5.2.3 GENERAL LORENTZ TRANSFORMATION 81
5.3 GROUP OF CONFORMAL TRANSFORMATIONS 82
5.3.1 DEFINITIONS 82
5.3.2 PROPERTIES OF CONFORMAL TRANSFORMATIONS 83
CONTENTS
XI
5.3.3 TRANSFORMATION OF MULTIVECTORS 84
5.4 DIRAC ALGEBRA 85
5.4.1 DIRAC EQUATION 85
5.4.2 UNITARY AND SYMPLECTIC UNITARY GROUPS 86
5.5 EXERCISES 88
6 SPECIAL RELATIVITY 91
6.1 LORENTZ TRANSFORMATION 91
6.1.1 SPECIAL LORENTZ TRANSFORMATION 91
6.1.2 PHYSICAL CONSEQUENCES 92
6.1.3 GENERAL LORENTZ TRANSFORMATION 94
6.2 RELATIVISTIC KINEMATICS 94
6.2.1 FOUR-VECTORS 94
6.2.2 ADDITION OF VELOCITIES 97
6.3 RELATIVISTIC DYNAMICS OF A POINT MASS 99
6.3.1 FOUR-MOMENTUM 99
6.3.2 FOUR-FORCE 100
6.4 EXERCISES 103
7 CLASSICAL ELECTROMAGNETISM 105
7.1 ELECTROMAGNETIC QUANTITIES 105
7.1.1 FOUR-CURRENT DENSITY AND FOUR-POTENTIAL 105
7.1.2 ELECTROMAGNETIC FIELD BIVECTOR 107
7.2 MAXWELL'S EQUATIONS 110
7.2.1 DIFFERENTIAL FORMULATION 110
7.2.2 INTEGRAL FORMULATION 115
7.2.3 LORENTZ FORCE 116
7.3 ELECTROMAGNETIC WAVES 118
7.3.1 ELECTROMAGNETIC WAVES IN VACUUM 118
7.3.2 ELECTROMAGNETIC WAVES IN A CONDUCTOR 119
7.3.3 ELECTROMAGNETIC WAVES IN A PERFECT MEDIUM 120
7.4 RELATIVISTIC OPTICS 121
7.4.1 FIZEAU EXPERIMENT (1851) 121
7.4.2 DOPPLER EFFECT 123
7.4.3 ABERRATION OF DISTAN
T STAR
S 124
7.5 EXERCISES 125
8 GENERAL RELATIVITY 127
8.1 RIEMANNIAN SPACE 127
8.2 EINSTEIN'S EQUATIONS 128
8.3 EQUATION OF MOTION 129
8.4 APPLICATIONS 130
8.4.1 SCHWARZSCHILD METRIC 130
8.4.2 LINEAR APPROXIMATION 133
XII
CONTENTS
CONCLUSION 135
A SOLUTIONS 137
B FORMULARY: MULTIVECTOR PRODUCTS WITHIN H(C) 153
C FORMULARY: MULTIVECTOR PRODUCTS WITHIN H H (OVER R) 157
D FORMULARY: FOUR-NABLA OPERATOR V WITHIN HI H (OVER R) 161
E WORK-SHEET: H(C) (MATHEMATICA) 163
F WORK-SHEET H
U
OVER R (MATHEMATICA) 165
G WORK-SHEET: MATRICES M
2
(H) (MATHEMATICA) 167
H CLIFFORD ALGEBRAS: ISOMORPHISMS 169
I CLIFFORD ALGEBRAS: SYNOPTIC TABLE 171
BIBLIOGRAPHY 173
INDEX 177 |
| adam_txt |
PATRICK R. GIRARD
QUATERNIONS,
FFORD ALGEBRA
S AN
D
SLATIVISTI
C PHYSIC
S
BIRKHAUSER
BASEL BOSTON BERLIN
CONTENTS
INTRODUCTION 1
1 QUATERNIONS 3
1.1 GROUP STRUCTUR
E 3
1.2 FINITE GROUPS OF ORDER N 8 4
1.3 QUATERNION GROUP 7
1.4 QUATERNION ALGEBRA H 8
1.4.1 DEFINITIONS 8
1.4.2 POLAR FORM 11
1.4.3 SQUARE ROOT AND N
T
H
ROOT 11
1.4.4 OTHER FUNCTIONS AND REPRESENTATIONS OF QUATERNIONS 14
1.5 CLASSICAL VECTOR CALCULUS 15
1.5.1 SCALAR PRODUCT AND VECTOR PRODUCT 15
1.5.2 TRIPLE SCALAR AND DOUBLE VECTOR PRODUCTS 16
1.6 EXERCISES 17
2 ROTATION GROUPS
SO(4)
AND
SO(3)
19
2.1 ORTHOGONAL GROUPS 0(4
) AND S0(4
) 19
2.2 ORTHOGONAL GROUPS 0(3
) AND S0(3
) 22
2.3 CRYSTALLOGRAPHIC GROUPS 24
2.3.1 DOUBLE CYCLIC GROUPS
C
N
(ORDER
N = 2N)
24
2.3.2 DOUBLE DIHEDRAL GROUPS
D
N
(N = AN)
24
2.3.3 DOUBLE TETRAHEDRA
L GROUP
(N -
24) 25
2.3.4 DOUBLE OCTAHEDRAL GROUP
(N =
48) 26
2.3.5 DOUBLE ICOSAHEDRAL GROUP
(N =
120) 27
2.4 INFINITESIMAL TRANSFORMATIONS OF SO(4) 28
2.5 SYMMETRIES AND INVARIANTS: KEPLER'S PROBLEM 32
2.6 EXERCISES 34
3 COMPLEX QUATERNIONS 37
3.1 ALGEBRA OF COMPLEX QUATERNIONS H(C) 37
3.2 LORENTZ GROUPS 0(1,3
) AND SO(1,3) 38
3.2.1 METRIC 38
CONTENTS
3.2.2 PLANE SYMMETRY 38
3.2.3 GROUPS 0(1,3
) AND S0(L,3
) 39
3.3 ORTHOCHRONOUS, PROPER LORENTZ GROUP 41
3.3.1 PROPERTIES 41
3.3.2 INFINITESIMAL TRANSFORMATIONS OF SO(1,3) 43
3.4 FOUR-VECTORS AND MULTIVECTORS IN H(C) 44
3.5 RELATIVISTIC KINEMATICS VIA H(C) 47
3.5.1 SPECIAL LORENTZ TRANSFORMATION 47
3.5.2 GENERAL PURE LORENTZ TRANSFORMATION 48
3.5.3 COMPOSITION OF VELOCITIES 48
3.6 MAXWELL'S EQUATIONS 50
3.7 GROUP OF CONFORMAL TRANSFORMATIONS 52
3.8 EXERCISES 54
CLIFFORD ALGEBRA 57
4.1 CLIFFORD ALGEBRA 57
4.1.1 DEFINITIONS 57
4.1.2 CLIFFORD ALGEBRA H
G HI OVER R 58
4.2 MULTIVECTOR CALCULUS WITHIN H H 59
4.2.1 EXTERIOR AND INTERIOR PRODUCTS WITH A VECTOR 59
4.2.2 PRODUCT
S OF TWO MULTIVECTORS 61
4.2.3 GENERAL FORMULAS 62
4.2.4 CLASSICAL VECTOR CALCULUS 64
4.3 MULTIVECTOR GEOMETRY 64
4.3.1 ANALYTIC GEOMETRY 64
4.3.2 ORTHOGONAL PROJECTIONS 66
4.4 DIFFERENTIAL OPERATORS 69
4.4.1 DEFINITIONS 69
4.4.2 INFINITESIMAL ELEMENTS OF CURVES, SURFACES AND HYPERSURFACES 69
4.4.3 GENERAL THEOREMS 71
4.5 EXERCISES 72
SYMMETRY GROUPS 75
5.1 PSEUDO-ORTHOGONAL GROUPS 0(1,3
) AND SO(1,3) 75
5.1.1 METRIC 75
5.1.2 SYMMETRY WITH RESPECT T
O A HYPERPLANE 75
5.1.3 PSEUDO-ORTHOGONAL GROUPS 0(1,3
) AND S0(L
, 3) 77
5.2 PROPER ORTHOCHRONOUS LORENTZ GROUP 78
5.2.1 ROTATION GROUP SO(3) 78
5.2.2 PUR
E LORENTZ TRANSFORMATION 79
5.2.3 GENERAL LORENTZ TRANSFORMATION 81
5.3 GROUP OF CONFORMAL TRANSFORMATIONS 82
5.3.1 DEFINITIONS 82
5.3.2 PROPERTIES OF CONFORMAL TRANSFORMATIONS 83
CONTENTS
XI
5.3.3 TRANSFORMATION OF MULTIVECTORS 84
5.4 DIRAC ALGEBRA 85
5.4.1 DIRAC EQUATION 85
5.4.2 UNITARY AND SYMPLECTIC UNITARY GROUPS 86
5.5 EXERCISES 88
6 SPECIAL RELATIVITY 91
6.1 LORENTZ TRANSFORMATION 91
6.1.1 SPECIAL LORENTZ TRANSFORMATION 91
6.1.2 PHYSICAL CONSEQUENCES 92
6.1.3 GENERAL LORENTZ TRANSFORMATION 94
6.2 RELATIVISTIC KINEMATICS 94
6.2.1 FOUR-VECTORS 94
6.2.2 ADDITION OF VELOCITIES 97
6.3 RELATIVISTIC DYNAMICS OF A POINT MASS 99
6.3.1 FOUR-MOMENTUM 99
6.3.2 FOUR-FORCE 100
6.4 EXERCISES 103
7 CLASSICAL ELECTROMAGNETISM 105
7.1 ELECTROMAGNETIC QUANTITIES 105
7.1.1 FOUR-CURRENT DENSITY AND FOUR-POTENTIAL 105
7.1.2 ELECTROMAGNETIC FIELD BIVECTOR 107
7.2 MAXWELL'S EQUATIONS 110
7.2.1 DIFFERENTIAL FORMULATION 110
7.2.2 INTEGRAL FORMULATION 115
7.2.3 LORENTZ FORCE 116
7.3 ELECTROMAGNETIC WAVES 118
7.3.1 ELECTROMAGNETIC WAVES IN VACUUM 118
7.3.2 ELECTROMAGNETIC WAVES IN A CONDUCTOR 119
7.3.3 ELECTROMAGNETIC WAVES IN A PERFECT MEDIUM 120
7.4 RELATIVISTIC OPTICS 121
7.4.1 FIZEAU EXPERIMENT (1851) 121
7.4.2 DOPPLER EFFECT 123
7.4.3 ABERRATION OF DISTAN
T STAR
S 124
7.5 EXERCISES 125
8 GENERAL RELATIVITY 127
8.1 RIEMANNIAN SPACE 127
8.2 EINSTEIN'S EQUATIONS 128
8.3 EQUATION OF MOTION 129
8.4 APPLICATIONS 130
8.4.1 SCHWARZSCHILD METRIC 130
8.4.2 LINEAR APPROXIMATION 133
XII
CONTENTS
CONCLUSION 135
A SOLUTIONS 137
B FORMULARY: MULTIVECTOR PRODUCTS WITHIN H(C) 153
C FORMULARY: MULTIVECTOR PRODUCTS WITHIN H H (OVER R) 157
D FORMULARY: FOUR-NABLA OPERATOR V WITHIN HI H (OVER R) 161
E WORK-SHEET: H(C) (MATHEMATICA) 163
F WORK-SHEET H
U
OVER R (MATHEMATICA) 165
G WORK-SHEET: MATRICES M
2
(H) (MATHEMATICA) 167
H CLIFFORD ALGEBRAS: ISOMORPHISMS 169
I CLIFFORD ALGEBRAS: SYNOPTIC TABLE 171
BIBLIOGRAPHY 173
INDEX 177 |
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| id | DE-604.BV022413151 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:22:50Z |
| indexdate | 2024-07-20T09:16:09Z |
| institution | BVB |
| isbn | 9783764377908 3764377909 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015621604 |
| oclc_num | 82148948 |
| open_access_boolean | |
| owner | DE-706 DE-703 DE-11 DE-188 |
| owner_facet | DE-706 DE-703 DE-11 DE-188 |
| physical | XII, 179 S. graph. Darst. 24 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Girard, Patrick R. Verfasser aut Quaternions, algèbre de Clifford et physique relativiste Quaternions, Clifford algebras and relativistic physics Patrick R. Girard Basel ; Boston ; Berlin Birkhäuser 2007 XII, 179 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 173 - 176 Clifford, Algèbres de Quaternions Clifford algebras Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf Quaternion (DE-588)4176653-2 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Elektrodynamik (DE-588)4014251-6 gnd rswk-swf Quaternion (DE-588)4176653-2 s Clifford-Algebra (DE-588)4199958-7 s Relativitätstheorie (DE-588)4049363-5 s Elektrodynamik (DE-588)4014251-6 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2857054&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=015621604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Girard, Patrick R. Quaternions, Clifford algebras and relativistic physics Clifford, Algèbres de Quaternions Clifford algebras Clifford-Algebra (DE-588)4199958-7 gnd Quaternion (DE-588)4176653-2 gnd Relativitätstheorie (DE-588)4049363-5 gnd Elektrodynamik (DE-588)4014251-6 gnd |
| subject_GND | (DE-588)4199958-7 (DE-588)4176653-2 (DE-588)4049363-5 (DE-588)4014251-6 |
| title | Quaternions, Clifford algebras and relativistic physics |
| title_alt | Quaternions, algèbre de Clifford et physique relativiste |
| title_auth | Quaternions, Clifford algebras and relativistic physics |
| title_exact_search | Quaternions, Clifford algebras and relativistic physics |
| title_exact_search_txtP | Quaternions, Clifford algebras and relativistic physics |
| title_full | Quaternions, Clifford algebras and relativistic physics Patrick R. Girard |
| title_fullStr | Quaternions, Clifford algebras and relativistic physics Patrick R. Girard |
| title_full_unstemmed | Quaternions, Clifford algebras and relativistic physics Patrick R. Girard |
| title_short | Quaternions, Clifford algebras and relativistic physics |
| title_sort | quaternions clifford algebras and relativistic physics |
| topic | Clifford, Algèbres de Quaternions Clifford algebras Clifford-Algebra (DE-588)4199958-7 gnd Quaternion (DE-588)4176653-2 gnd Relativitätstheorie (DE-588)4049363-5 gnd Elektrodynamik (DE-588)4014251-6 gnd |
| topic_facet | Clifford, Algèbres de Quaternions Clifford algebras Clifford-Algebra Quaternion Relativitätstheorie Elektrodynamik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2857054&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015621604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT girardpatrickr quaternionsalgebredecliffordetphysiquerelativiste AT girardpatrickr quaternionscliffordalgebrasandrelativisticphysics |