物理學傢用的幾何代數 [Geometric Algebra for Physicists] 下載 mobi epub pdf 電子書 2024

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　　《物理學傢用的幾何代數》包括導論；二維和三維的幾何代數；經典力學；幾何代數基礎；相對性和時空；幾何微積分；經典電動力學；量子論和自鏇；多粒子態和量子糾纏；幾何；微積分和群論中的高等論題；拉格朗日和哈密爾頓技巧；對稱和規範理論；引力。《物理學傢用的幾何代數》讀者對象：物理、幾何代數專業的學生、老師和相關的科研人員。

內容簡介

　　《物理學傢用的幾何代數》是一部不僅讓對物理學感興趣的讀者的讀物，也是一本對物理現實感興趣的讀者的讀物。幾何代數在過去的十年中得到瞭快速發展，成為物理和工程領域的一個重要課題。作者是該領域的一個領頭人物，做瞭許多重大進展。書中帶領讀者走進該領域，其中包括好多應用，黑洞物理學和量子計算，非常適於作為一本幾何代數物理應用方麵的研究生教程。

內頁插圖

目錄

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

物理學傢用的幾何代數 [Geometric Algebra for Physicists] 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

評分☆☆☆☆☆

一本學習幾何代數的好書，內容係統、全麵。買來放書桌上，閑時翻翻，多少會有些收獲。

評分☆☆☆☆☆

不錯的幾本書，介紹物理中用到的一些數學知識

評分☆☆☆☆☆

這是一部不僅讓對物理學感興趣的讀者的讀物，也是一本對物理現實感興趣的讀者的讀物。幾何代數在過去的十年中得到瞭快速發展，成為物理和工程領域的一個重要課題。作者是該領域的一個領頭人物，做瞭許多重大進展。書中帶領讀者走進該領域，其中包括好多應用，黑洞物理學和量子計算，非常適於作為一本幾何代數物理應用方麵的研究生教程。

評分☆☆☆☆☆

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個人謹慎推薦。

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講瞭很多其他專門寫給物理學傢的數學書沒有的內容

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比較好的書籍，買來當參考書。

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值得推薦的經典教材！

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