目录

Lie Groups in Physics | 夫风生于地，起于青蘋之末

2022-10-26

1分钟阅读时长

数学 , 笔记

总目录:

Chapter 1 : A brief introduction from geometric perspective

§1 Lie groups as manifolds

1.1 Endowed structures

1.2 Examples

§2 Lie algebras as sets of vector fields

2.1 Left-invariant vector fields

2.2 The Lie algebra of a Lie group

2.3 Maurer-Cartan’s structure equation

§3 Exponential mapping unto flows

3.1 One-parameter subgroups of Lie groups

3.2 One-parameter groups of transformations generated by vector fields

3.3 The exponential mapping & some calculations

§4 Action of Lie groups on other manifolds

4.1 Definitions

4.2 Orbits and stabilizers

4.3 Homogeneous spaces and examples

Chapter 2 : Some algebras

Chapter 3 : Quiz: SO(3), SU(2) and quantum mechanics

Chapter 4 : Particle physics in the mist

Chapter 5 : More algebras

Chapter 6 : Spacetime symmetries: the Lorentz and Poincaré groups

Chapter 7 : The Standard Model and the SU(5) Grand Unification

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H. Bai 当我们直立而面对现实的时候，能够看到太阳的两面都在熠熠生辉。