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Lie Groups in Physics | 夫风生于地,起于青蘋之末
  • Chapter 1 : A brief introduction from geometric perspective
  • Chapter 2 : Some algebras

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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