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Currently Playing: Spinors for Beginners 18: Irreducible Representations of SU(2) (Ladder Operators)

Full spinors playlist: https://www.youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBs Leave me a tip: https://ko-fi.com/eigenchris Powerpoint slide files + Exercise answers: https://github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners Wikipedia page with example su(2) reps: https://en.wikipedia.org/wiki/3D_rotation_group Wikipedia page about spin angular momentum of light: https://en.wikipedia.org/wiki/Spin_angular_momentum_of_light Wikipedia page on helicity in particle physics (and gravitational waves):https://en.wikipedia.org/wiki/Helicity_(particle_physics)#:~:text=A%20treatment%20of%20the%20helicity%20of%20gravitational%20waves,(they%20can%20be%20removed%20by%20a%20gauge%20transformation) Weinberg book of gravitation (see Chapter 10.8 on gravitational wave helicity): https://archive.org/details/WeinbergS.GravitationAndCosmology..PrinciplesAndApplicationsOfTheGeneralTheoryOf 0:00 - Introduction 0:59 - Representation Theory Definitions 3:45 - Irreducible Representations 6:00 - Ladder Operators (2x2) 10:27 - Ladder Commutators 13:12 - Raising/Lowering Eigenvectors 18:00 - Casimir Operator 24:13 - Highest Weight Eigenvector 25:25 - Spin-1 irrep of su(2) 30:30 - Spin-3/2 and Spin-2 irreps of su(2) 32:12 - Rotating Particles 35:23 - Proof of one SU(2) irrep per dimension 36:46 - One SO(3) irrep per odd dimension 41:07 - Differential / Polynomial representations 41:49 - Irreps of sl(2,C)