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物理学家用的几何代数 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （英）多兰（DoranC）著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510078552
- 出版时间：2014
- 标注页数：578页
- 文件大小：71MB
- 文件页数：593页
- 主题词：几何学－英文；代数－英文
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图书目录
1 Introduction1
1.1 Vector(linear)spaces2
1.2 The scalar product4
1.3 Complex numbers6
1.4 Quaternions7
1.5 The cross product10
1.6 The outer product11
1.7 Notes17
1.8 Exercises18
2 Geometric algebra in two and three dimensions20
2.1 A new product for vectors21
2.2 An outline of geometric algebra23
2.3 Geometric algebra of the plane24
2.4 The geometric algebra of space29
2.5 Conventions38
2.6 Reflections40
2.7 Rotations43
2.8 Notes51
2.9 Exercises52
3 Classical mechanics54
3.1 Elementary principles55
3.2 Two-body central force interactions59
3.3 Celestial mechanics and perturbations64
3.4 Rotating systems and rigid-body motion69
3.5 Notes81
3.6 Exercises82
4 Foundations of geometric algebra84
4.1 Axiomatic development85
4.2 Rotations and reflections97
4.3 Bases,frames and components100
4.4 Linear algebra103
4.5 Tensors and components115
4.6 Notes122
4.7 Exercises124
5 Relativity and spacetime126
5.1 An algebra for spacetime127
5.2 Observers,trajectories and frames131
5.3 Lorentz transformations138
5.4 The Lorentz group143
5.5 Spacetime dynamics150
5.6 Notes163
5.7 Exercises164
6 Geometric calculus167
6.1 The vector derivative168
6.2 Curvilinear coordinates173
6.3 Analytic functions178
6.4 Directed integration theory183
6.5 Embedded surfaces and vector manifolds202
6.6 Elasticity220
6.7 Notes224
6.8 Exercises225
7 Classical electrodynamics228
7.1 Maxwell's equations229
7.2 Integral and conservation theorems235
7.3 The electromagnetic field of a point charge241
7.4 Electromagnetic waves251
7.5 Scattering and diffraction258
7.6 Scattering261
7.7 Notes264
7.8 Exercises265
8 Quantum theory and spinors267
8.1 Non-relativistic quantum spin267
8.2 Relativistic quantum states278
8.3 The Dirac equation281
8.4 Central potentials288
8.5 Scattering theory297
8.6 Notes305
8.7 Exercises307
9 Multiparticle states and quantum entanglement309
9.1 Many-body quantum theory310
9.2 Multiparticle spacetime algebra315
9.3 Systems of two particles319
9.4 Relativistic states and operators325
9.5 Two-spinor calculus332
9.6 Notes337
9.7 Exercises337
10 Geometry340
10.1 Projective geometry341
10.2 Conformal geometry351
10.3 Conformal transformations355
10.4 Geometric primitives in conformal space360
10.5 Intersection and reflection in conformal space365
10.6 Non-Euclidean geometry370
10.7 Spacetime conformal geometry383
10.8 Notes390
10.9 Exercises391
11 Further topics in calculus and group theory394
11.1 Multivector calculus394
11.2 Grassmann calculus399
11.3 Lie groups401
11.4 Complex structures and unitary groups408
11.5 The general linear group412
11.6 Notes416
11.7 Exercises417
12 Lagrangian and Hamiltonian techniques420
12.1 The Euler-Lagrange equations421
12.2 Classical models for spin-1/2 particles427
12.3 Hamiltonian techniques432
12.4 Lagrangian field theory439
12.5 Notes444
12.6 Exercises445
13 Symmetry and gauge theory448
13.1 Conservation laws in field theory449
13.2 Electromagnetism453
13.3 Dirac theory457
13.4 Gauge principles for gravitation466
13.5 The gravitational field equations474
13.6 The structure of the Riemann tensor490
13.7 Notes495
13.8 Exercises495
14 Gravitation497
14.1 Solving the field equations498
14.2 Spherically-symmetric systems500
14.3 Schwarzschild black holes510
14.4 Quantum mechanics in a black hole background524
14.5 Cosmology535
14.6 Cylindrical systems543
14.7 Axially-symmetric systems551
14.8 Notes564
14.9 Exercises565
Bibliography568
Index575