Geometric algebra for physicists:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2007
|
| Ausgabe: | 1. paperback ed. publ. with corr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 568-574) and index |
| Beschreibung: | XIV, 578 S. Ill., graph. Darst. |
| ISBN: | 9780521715959 0521715954 9780521480222 0521480221 |
Internformat
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| 245 | 1 | 0 | |a Geometric algebra for physicists |c Chris Doran and Anthony Lasenby |
| 250 | |a 1. paperback ed. publ. with corr. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 2007 | |
| 300 | |a XIV, 578 S. |b Ill., graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 500 | |a Includes bibliographical references (p. 568-574) and index | ||
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| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Mathematical physics | |
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Datensatz im Suchindex
| _version_ | 1804137230763032576 |
|---|---|
| adam_text | Contents
Preface ix
Notation xiii
1 Introduction 1
1.1 Vector (linear) Spaces 2
1.2 The scalar product 4
1.3 Complex numbers 6
1.4 Quaternions 7
1.5 The cross product 10
1.6 The outer product 11
1.7 Notes 17
1.8 Exercises 18
2 Geometrie algebra in two and three dimensions 20
2.1 A new product for vectors 21
2.2 An outline of geometric algebra 23
2.3 Geometrie algebra of the plane 24
2.4 The geometric algebra of space 29
2.5 Conventions 38
2.6 Reflections 40
2.7 Rotations 43
2.8 Notes 51
2.9 Exercises 52
3 Classical mechanics 54
3.1 Elementary principles 55
3.2 Two-body central force interactions 59
3.3 Celestial mechanics and Derturbations 64
CONTENTS
3.4 Rotating systems and rigid-body motion
3.5 Notes
3.6 Exercises
4 Foundations of geometric algebra
4.1 Axiomatic development
4.2 Rotations and reflections
4.3 Bases, frames and components
4.4 Linear algebra
4.5 Tensors and components
4.6 Notes
4.7 Exercises
5 Relativity and spacetime
5.1 An algebra for spacetime
5.2 Observers, trajectories and frames
5.3 Lorentz transformations
5.4 The Lorentz group
5.5 Spacetime dynamics
5.6 Notes
5.7 Exercises
6 Geometric calculus
6.1 The vector derivative
6.2 Curvilinear coordinates
6.3 Analytic functions
6.4 Directed integration theory
6.5 Embedded surfaces and vector manifolds
6.6 Elasticity
6.7 Notes
6.8 Exercises
7 Classical electrodynamics
7.1 Maxwell s equations
7.2 Integral and conservation theorems
7.3 The electromagnetic field of a point charge
7.4 Electromagnetic waves
7.5 Scattering and diffraction
7.6 Scattering
7.7 Notes
7.8 Exercises
69
81
82
84
85
97
100
103
115
122
124
126
127
131
138
143
150
163
164
167
168
173
178
183
202
220
224
225
228
229
235
241
251
258
261
264
265
CONTENTS
8 Quantum theory and spinors 267
8.1 Non-relativistic quantum spin 267
8.2 Relativistic quantum states 278
8.3 The Dirac equation 281
8.4 Central potentials 288
8.5 Scattering theory 297
8.6 Notes 305
8.7 Exercises 307
9 Multiparticle states and quantum entanglement 309
9.1 Many-body quantum theory 310
9.2 Multiparticle spacetime algebra 315
9.3 Systems of two particles 319
9.4 Relativistic states and Operators 325
9.5 Two-spinor calculus 332
9.6 Notes 337
9.7 Exercises 337
10 Geometry 340
10.1 Projective geometry 341
10.2 Conformal geometry 351
10.3 Conformal transformations 355
10.4 Geometrie primitives in conformal space 360
10.5 Intersection and reflection in conformal space 365
10.6 Non-Euclidean geometry 370
10.7 Spacetime conformal geometry 383
10.8 Notes 390
10.9 Exercises 391
11 Further topics in calculus and group theory 394
11.1 Multivector calculus 394
11.2 Grassmann calculus 399
11.3 Lie groups 401
11.4 Complex struetures and unitary groups 408
11.5 The general linear group 412
11.6 Notes 416
11.7 Exercises 417
12 Lagrangian and Hamiltonian techniques 420
12.1 The Euler-Lagrange equations 421
12.2 Classical modeis for spin-1/2 particles 427
12.3 Hamiltonian techniques 432
CONTENTS
12.4 Lagrangian field theory 439
12.5 Notes 444
12.6 Exercises 445
13 Symmetry and gauge theory 448
13.1 Conservation laws in field theory 449
13.2 Electromagnetism 453
13.3 Dirac theory 457
13.4 Gauge principles for gravitation 466
13.5 The gravitational field equations 474
13.6 The structure of the Riemann tensor 490
13.7 Notes 495
13.8 Exercises 495
14 Gravitation 497
14.1 Solving the field equations 498
14.2 Spherically-symmetric systems 500
14.3 Schwarzschild black holes 510
14.4 Quantum mechanics in a black hole background 524
14.5 Cosmology 535
14.6 Cylindrical systems 543
14.7 Axially-symmetric systems 551
14.8 Notes 564
14.9 Exercises 565
Bibliography 568
Index 575
vm
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| adam_txt |
Contents
Preface ix
Notation xiii
1 Introduction 1
1.1 Vector (linear) Spaces 2
1.2 The scalar product 4
1.3 Complex numbers 6
1.4 Quaternions 7
1.5 The cross product 10
1.6 The outer product 11
1.7 Notes 17
1.8 Exercises 18
2 Geometrie algebra in two and three dimensions 20
2.1 A new product for vectors 21
2.2 An outline of geometric algebra 23
2.3 Geometrie algebra of the plane 24
2.4 The geometric algebra of space 29
2.5 Conventions 38
2.6 Reflections 40
2.7 Rotations 43
2.8 Notes 51
2.9 Exercises 52
3 Classical mechanics 54
3.1 Elementary principles 55
3.2 Two-body central force interactions 59
3.3 Celestial mechanics and Derturbations 64
CONTENTS
3.4 Rotating systems and rigid-body motion
3.5 Notes
3.6 Exercises
4 Foundations of geometric algebra
4.1 Axiomatic development
4.2 Rotations and reflections
4.3 Bases, frames and components
4.4 Linear algebra
4.5 Tensors and components
4.6 Notes
4.7 Exercises
5 Relativity and spacetime
5.1 An algebra for spacetime
5.2 Observers, trajectories and frames
5.3 Lorentz transformations
5.4 The Lorentz group
5.5 Spacetime dynamics
5.6 Notes
5.7 Exercises
6 Geometric calculus
6.1 The vector derivative
6.2 Curvilinear coordinates
6.3 Analytic functions
6.4 Directed integration theory
6.5 Embedded surfaces and vector manifolds
6.6 Elasticity
6.7 Notes
6.8 Exercises
7 Classical electrodynamics
7.1 Maxwell's equations
7.2 Integral and conservation theorems
7.3 The electromagnetic field of a point charge
7.4 Electromagnetic waves
7.5 Scattering and diffraction
7.6 Scattering
7.7 Notes
7.8 Exercises
69
81
82
84
85
97
100
103
115
122
124
126
127
131
138
143
150
163
164
167
168
173
178
183
202
220
224
225
228
229
235
241
251
258
261
264
265
CONTENTS
8 Quantum theory and spinors 267
8.1 Non-relativistic quantum spin 267
8.2 Relativistic quantum states 278
8.3 The Dirac equation 281
8.4 Central potentials 288
8.5 Scattering theory 297
8.6 Notes 305
8.7 Exercises 307
9 Multiparticle states and quantum entanglement 309
9.1 Many-body quantum theory 310
9.2 Multiparticle spacetime algebra 315
9.3 Systems of two particles 319
9.4 Relativistic states and Operators 325
9.5 Two-spinor calculus 332
9.6 Notes 337
9.7 Exercises 337
10 Geometry 340
10.1 Projective geometry 341
10.2 Conformal geometry 351
10.3 Conformal transformations 355
10.4 Geometrie primitives in conformal space 360
10.5 Intersection and reflection in conformal space 365
10.6 Non-Euclidean geometry 370
10.7 Spacetime conformal geometry 383
10.8 Notes 390
10.9 Exercises 391
11 Further topics in calculus and group theory 394
11.1 Multivector calculus 394
11.2 Grassmann calculus 399
11.3 Lie groups 401
11.4 Complex struetures and unitary groups 408
11.5 The general linear group 412
11.6 Notes 416
11.7 Exercises 417
12 Lagrangian and Hamiltonian techniques 420
12.1 The Euler-Lagrange equations 421
12.2 Classical modeis for spin-1/2 particles 427
12.3 Hamiltonian techniques 432
CONTENTS
12.4 Lagrangian field theory 439
12.5 Notes 444
12.6 Exercises 445
13 Symmetry and gauge theory 448
13.1 Conservation laws in field theory 449
13.2 Electromagnetism 453
13.3 Dirac theory 457
13.4 Gauge principles for gravitation 466
13.5 The gravitational field equations 474
13.6 The structure of the Riemann tensor 490
13.7 Notes 495
13.8 Exercises 495
14 Gravitation 497
14.1 Solving the field equations 498
14.2 Spherically-symmetric systems 500
14.3 Schwarzschild black holes 510
14.4 Quantum mechanics in a black hole background 524
14.5 Cosmology 535
14.6 Cylindrical systems 543
14.7 Axially-symmetric systems 551
14.8 Notes 564
14.9 Exercises 565
Bibliography 568
Index 575
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| index_date | 2024-07-02T19:10:45Z |
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| institution | BVB |
| isbn | 9780521715959 0521715954 9780521480222 0521480221 |
| language | English |
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| physical | XIV, 578 S. Ill., graph. Darst. |
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| spelling | Doran, Chris Verfasser (DE-588)1194022332 aut Geometric algebra for physicists Chris Doran and Anthony Lasenby 1. paperback ed. publ. with corr. Cambridge [u.a.] Cambridge University Press 2007 XIV, 578 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 568-574) and index Mathematische Physik Geometry, Algebraic Mathematical physics Geometrische Algebra (DE-588)4156707-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Geometrische Algebra (DE-588)4156707-9 s Mathematische Physik (DE-588)4037952-8 s DE-604 Lasenby, Anthony 1954- Sonstige (DE-588)173634834 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016218732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Doran, Chris Geometric algebra for physicists Mathematische Physik Geometry, Algebraic Mathematical physics Geometrische Algebra (DE-588)4156707-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4156707-9 (DE-588)4037952-8 |
| title | Geometric algebra for physicists |
| title_auth | Geometric algebra for physicists |
| title_exact_search | Geometric algebra for physicists |
| title_exact_search_txtP | Geometric algebra for physicists |
| title_full | Geometric algebra for physicists Chris Doran and Anthony Lasenby |
| title_fullStr | Geometric algebra for physicists Chris Doran and Anthony Lasenby |
| title_full_unstemmed | Geometric algebra for physicists Chris Doran and Anthony Lasenby |
| title_short | Geometric algebra for physicists |
| title_sort | geometric algebra for physicists |
| topic | Mathematische Physik Geometry, Algebraic Mathematical physics Geometrische Algebra (DE-588)4156707-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Geometry, Algebraic Mathematical physics Geometrische Algebra |
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