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Currently Playing: Spinors for Beginners 17: The spin 1/2 representations of SU(2) and SL(2,C)

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 Physics of the Lorentz Group PDF (hints at how to re-write tensor product representation): https://iopscience.iop.org/book/mono/978-1-6817-4254-0.preview.pdf Previous videos: SfB #6.1 on Bivector-Quaternion equivalence: https://www.youtube.com/watch?v=0w5QnhS_55U SfB #9 on Weyl Spinors: https://www.youtube.com/watch?v=4NJBvkjpC3E SfB #10 Double Cover of SO(3): https://www.youtube.com/watch?v=Ay482u6b3Xo SfB #12 Spin Groups: https://www.youtube.com/watch?v=AFwc0DPoFe8 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)