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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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