引力 : 基础与前沿

List of exercises

List of projects

Preface

How to use this book

1　Special relativity

1.1 Introduction

1.2 The principles of special relativity

1.3 Transformation of coordinates and velocities

1.3.1 Lorentz transformation

1.3.2 Transformation of velocities

1.3.3 Lorentz boost in an arbitrary direction

1.4 Four-vectors

1.4.1 Four-velocity and acceleration

1.5 Tensors

1.6 Tensors as geometrical objects

List of exercises

List of projects

Preface

How to use this book

1　Special relativity

1.1   Introduction

1.2  The principles of special relativity

1.3  Transformation of coordinates and velocities

1.3.1  Lorentz transformation

1.3.2  Transformation of velocities

1.3.3  Lorentz boost in an arbitrary direction

1.4  Four-vectors

1.4.1  Four-velocity and acceleration

1.5  Tensors

1.6  Tensors as geometrical objects

1.7  Volume and surface integrals in four dimensions

1.8  Particle dynamics

1.9  The distribution function and its moments

1.10 The Lorentz group and Pauli matrices

2　Scalar and electromagnetic fields in special relativity

2.1  Introduction

2.2  External fields of force

2.3  Classical scalar field

2.3.1  Dynamics of a particle interacting with a scalar

field

2.3.2  Action and dynamics of the scalar field

2.3.3  Energy-momentum tensor for the scalar field

2.3.4  Free field and the wave solutions

2.3.5  Why does the scalar field lead to an attractive

force?

2.4  Electromagnetic field

2.4.1  Charged particle in an electromagnetic field

2.4.2  Lorentz transformation of electric and magnetic

fields

2.4.3  Current vector

2.5   Motion in the Coulomb field

2.6  Motion in a constant electric field

2.7  Action principle for the vector field

2.8   Maxwell's equations

2.9  Energy and momentum of the electromagnetic field

2.10 Radiation from an accelerated charge

2.11  Larmor formula and radiation reaction

3　Gravity and spaeetime geometry: the inescapable connection

3.1   Introduction

3.2  Field theoretic approaches to gravity

3.3   Gravity as a scalar field

3.4   Second rank tensor theory of gravity

3.5   The principle of equivalence and the geometrical

description　of gravity

3.5.1  Uniformly accelerated observer

3.5.2  Gravity and the flow of time

4　Metric tensor, geodesics and covariant derivative

4.1   Introduction

4.2  Metric tensor and gravity

4.3   Tensor algebra in curved spacetime

4.4  Volume and surface integrals

4.5   Geodesic curves

4.5.1  Properties of geodesic curves

4.5.2  Affine parameter and null geodesics

4.6  Covariant derivative

4.6.1  Geometrical interpretation of the covariant

derivative

4.6.2  Manipulation of covariant derivatives

4.7   Parallel transport

4.8   Lie transport and Killing vectors

4.9   Fermi-Walker transport

5　Curvature of spaeetime

5.1   Introduction

5.2   Three perspectives on the spacetime

curvature

5.2.1  Parallel transport around a closed curve

5.2.2  Non-commutativity of covariant derivatives

……

《Gravitation：Foundations and Frontiers引力——基础与前沿（影印版）》覆盖了当代引力理论的方方面面。在基础部分，本书首先介绍了引力理论的一些基本的概念、方法和公式。之后，本书进而对引力理论在球对称时空、黑洞、引力波和宇宙学领域的应用做了系统而深入的介绍。在前沿部分，本书讨论了宇宙微扰论、弯曲时空量子场论和广义相对论的Hamiltonian结构等当前很受关注的重要问题。本书适合理论物理所有领域的研究者和研究生阅读。