物理学家用的几何代数 [Geometric Algebra for Physicists] epub pdf mobi txt 电子书 下载 2024

物理学家用的几何代数 [Geometric Algebra for Physicists] epub pdf mobi txt 电子书 下载 2024

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物理学家用的几何代数 [Geometric Algebra for Physicists] epub pdf mobi txt 电子书 下载 2024

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　　《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。

内容简介

　　《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。

内页插图

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

前言/序言

物理学家用的几何代数 [Geometric Algebra for Physicists] epub pdf mobi txt 电子书 下载 2024

物理学家用的几何代数 [Geometric Algebra for Physicists] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

评分☆☆☆☆☆

几何代数算是一种不同于我们已经习惯的描述物理理论的数学工具，有人试图把我们已知的物理理论都用几何代数的语言来写，早先科学出版社就影印出版过一本《经典力学的新基础》，书中就是用几何代数的语言写的经典力学。有一定的参考性。

评分☆☆☆☆☆

评分☆☆☆☆☆

比较好的书籍，买来当参考书。

评分☆☆☆☆☆

几何代数算是一种不同于我们已经习惯的描述物理理论的数学工具，有人试图把我们已知的物理理论都用几何代数的语言来写，早先科学出版社就影印出版过一本《经典力学的新基础》，书中就是用几何代数的语言写的经典力学。有一定的参考性。

评分☆☆☆☆☆

个人谨慎推荐。

评分☆☆☆☆☆

值得推荐的经典教材！

评分☆☆☆☆☆

此书海外原版很贵的，需要两千多元人民币，在中国大陆印刷，纸张一般，但性价比很高！几年后此书会被疯抢至缺货的，因为研究几何代收的人会一下子多起来。

评分☆☆☆☆☆

一本介绍代数几何在物理学中应用的书，经典的好书。

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