物理学家用的几何代数

PrefaceNotation1 Introduction1.1 Vector （linear） spaces1.2 The scalar product1.3 Complex numbers1.4 Quaternions1.5 The cross product1.6 The outer product1.7 Notes1.8 Exercises2 Geometric algebra in two and three dimensions2.1 A new product for vectors2.2 An outline of geometric algebra2.3 Geometric algebra of the plane2.4 The geometric algebra of space2.5 Conventions2.6 Reflections2.7 Rotations2.8 Notes2.9 Exercises3 Classical mechanics3.1 Elementary principles3.2 Two—body central force interactions3.3 Celestial mechanics and perturbations3.4 Rotating systems and rigid—body motion3.5 Notes3.6 Exercises4 Foundations of geometric algebra4.1 Axiomatic development4.2 Rotations and refiections4.3 Bases， frames and components4.4 Linear algebra4.5 Tensors and components4.6 Notes4.7 Exercises5 Relativity and spacetime5.1 An algebra for spacetime5.2 Observers， trajectories and frames5.3 Lorentz transformations5.4 The Lorentz group5.5 Spacetime dynamics5.6 Notes5.7 Exercises6 Geometric calculus6.1 The vector derivative6.2 Curvilinear coordinates6.3 Analytic functions6.4 Directed integration theory6.5 Embedded surfaces and vector manifolds6.6 Elasticity6.7 Notes6.8 Exercises7 Classical electrodynamics7.1 Maxwell's equations7.2 Integral and conservation theorems7.3 The electromagnetic field of a point charge7.4 Electromagnetic waves7.5 Scattering and diffraction7.6 Scattering7.7 Notes7.8 Exercises8 Quantum theory and spinors8.1 Non—relativistic quantum spin8.2 Relativistic quantum states8.3 The Dirac equation8.4 Central potentials8.5 Scattering theory8.6 Notes8.7 Exercises9 Multiparticle states and quantum entanglement9.1 Many—body quantum theory9.2 Multiparticle spacetime algebra9.3 Systems of two particles9.4 Relativistic states and operators9.5 Two—spinor calculus9.6 Notes9.7 Exercises10 Geometry10.1 Projective geometry10.2 Conformal geometry10.3 Conformal transformations10.4 Geometric primitives in conformal space10.5 Intersection and reflection in conformal space10.6 Non—Euclidean geometry10.7 Spacetime conformal geometry10.8 Notes10.9 Exercises11 Further topics in calculus and group theory11.1 Multivector calculus11.2 Grassmann calculus11.3 Lie groups11.4 Complex structures and unitary groups11.5 The generallinear group11.6 Notes11.7 Exercises12 Lagrangian and Hamiltonian techniques12.1 The Euler—Lagrange equations12.2 Classical models for spin—1／2 particles12.3 Hamiltonian techniques12.4 Lagrangian field theory12.5 Notes12.6 Exercises13 Symmetry and gauge theory13.1 Conservation laws in field theory13.2 Electromagnetism13.3 Dirac theory13.4 Gauge principles for gravitation13.5 The gravitational field equations13.6 The structure of the Riemann tensor13.7 Notes13.8 Exercises14 Gravitation14.1 Solving the field equations14.2 Spherically—symmetric systems14.3 Schwarzschild black holes14.4 Quantum mechanics in a black hole background14.5 Cosmology14.6 Cylindrical systems14.7 Axially—symmetric systems14.8 Notes14.9 ExercisesBibliographyIndex

《物理学家用的几何代数》包括导论；二维和三维的几何代数；经典力学；几何代数基础；相对性和时空；几何微积分；经典电动力学；量子论和自旋；多粒子态和量子纠缠；几何；微积分和群论中的高等论题；拉格朗日和哈密尔顿技巧；对称和规范理论；引力。《物理学家用的几何代数》读者对象：物理、几何代数专业的学生、老师和相关的科研人员。《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。