Spinors for Beginners 17: The spin 1/2 representations of SU(2) and SL(2,C)
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Previous videos:
SfB #6.1 on Bivector-Quaternion equivalence: • Spinors for Beginners 6.1 - Equivale...
SfB #9 on Weyl Spinors: • Spinors for Beginners 9: Pauli Spinor...
SfB #10 Double Cover of SO(3): • Spinors for Beginners 10: SU(2) doubl...
SfB #12 Spin Groups: • Spinors for Beginners 12: How the Spi...
0:00 - Introduction + Review of SO(3)
1:39 - Spin-0 representation of SO(3)
4:16 - No spin-1/2 rep of SO(3)
5:04 - SU(2) is the double cover of SO(3)
7:10 - su(2) Lie Algebra
10:03 - su(2) commutation relations
12:30 - Exponentiating su(2) generators
15:50 - Rotations of 720 degrees
18:40 - Lorentz Group SO+(1,3)
20:44 - SL(2,C) and sl(2,C)
25:26 - Left and Right SL(2,C) representations
30:27 - (1/2, 1/2) tensor product representation
34:39 - Complexification of su(2) and sl(2,C)
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