- 物理学家用的几何代数(英文版)
- - 作者：(英)多兰
  - 出版社：世界图书出版公司
  - ISBN：9787510078552
  - 出版日期：2014/09/01
  - 页数：578
- 售价：59.6

内容大纲
《物理学家用的几何代数》是一部不仅让对物理学感兴趣的读者的读物，也是一本对物理现实感兴趣的读者的读物。几何代数在过去的十年中得到了快速发展，成为物理和工程领域的一个重要课题。作者多兰是该领域的一个领头人物，做了许多重大进展。书中带领读者走进该领域，其中包括好多应用，黑洞物理学和量子计算，非常适于作为一本几何代数物理应用方面的研究生教程。
作者介绍
目录
Preface
Notation
1 Introduction
  1.1 Vector （linear） spaces
  1.2 The scalar product
  1.3 Complex numbers
  1.4 Quaternions
  1.5 The cross product
  1.6 The outer product
  1.7 Notes
  1.8 Exercises
2 Geometric algebra in two and three dimensions
  2.1 A new product for vectors
  2.2 An outline of geometric algebra
  2.3 Geometric algebra of the plane
  2.4 The geometric algebra of space
  2.5 Conventions
  2.6 Reflections
  2.7 Rotations
  2.8 Notes
  2.9 Exercises
3 Classical mechanics
  3.1 Elementary principles
  3.2 Two-body central force interactions
  3.3 Celestial mechanics and perturbations
  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 refiections
  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
8 Quantum theory and spinors
  8.1 Non-relativistic quantum spin
  8.2 Relativistic quantum states
  8.3 The Dirac equation
  8.4 Central potentials
  8.5 Scattering theory
  8.6 Notes
  8.7 Exercises
9 Multiparticle states and quantum entanglement
  9.1 Many-body quantum theory
  9.2 Multiparticle spacetime algebra
  9.3 Systems of two particles
  9.4 Relativistic states and operators
  9.5 Two-spinor calculus
  9.6 Notes
  9.7 Exercises
10 Geometry
  10.1 Projective geometry
  10.2 Conformal geometry
  10.3 Conformal transformations
  10.4 Geometric primitives in conformal space
  10.5 Intersection and reflection in conformal space
  10.6 Non-Euclidean geometry
  10.7 Spacetime conformal geometry
  10.8 Notes
  10.9 Exercises
11 Further topics in calculus and group theory
  11.1 Multivector calculus
  11.2 Grassmann calculus
  11.3 Lie groups
  11.4 Complex structures and unitary groups
  11.5 The generallinear group
  11.6 Notes
  11.7 Exercises
12 Lagrangian and Hamiltonian techniques
  12.1 The Euler-Lagrange equations
  12.2 Classical models for spin-1／2 particles
  12.3 Hamiltonian techniques

  12.4 Lagrangian field theory
  12.5 Notes
  12.6 Exercises
13 Symmetry and gauge theory
  13.1 Conservation laws in field theory
  13.2 Electromagnetism
  13.3 Dirac theory
  13.4 Gauge principles for gravitation
  13.5 The gravitational field equations
  13.6 The structure of the Riemann tensor
  13.7 Notes
  13.8 Exercises
14 Gravitation
  14.1 Solving the field equations
  14.2 Spherically-symmetric systems
  14.3 Schwarzschild black holes
  14.4 Quantum mechanics in a black hole background
  14.5 Cosmology
  14.6 Cylindrical systems
  14.7 Axially-symmetric systems
  14.8 Notes
  14.9 Exercises
Bibliography
Index

内容大纲

作者介绍

目录

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