Spinors for Beginners 18: Irreducible Representations of SU(2) (Ladder Operators)
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Weinberg book of gravitation (see Chapter 10.8 on gravitational wave helicity): https://archive.org/details/WeinbergS...
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)
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