Spinors for Beginners 20: Lorentz Group / Algebra Representation Theory
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Powerpoint slide files + Exercise answers: https://github.com/eigenchris/MathNot...
Sources to look at:
Wikipedia article on "Representation Theory of the Lorentz Group": https://en.wikipedia.org/wiki/Represe...
"Group Theory for Physicsts" by Wu-Ki Tang
"Physics of the Lorentz Group, by Sibel Ba¸skal, Young S Kim, and Marilyn E Noz":
https://iopscience.iop.org/book/mono/...
0:00 - Review of SU(2) and SL(2,C)
6:39 - sl(2,C)c = su(2)c + su(2)c
10:28 - SL(2,C)c = SU(2)c x SU(2)c
12:30 - Representations of SL(2,C) and sl(2,C)
16:28 - J and K generator representations
18:55 - The scalar (0,0) irrep
20:32 - The spinor (1/2,0) and (0,1/2) irreps
25:08 - Dirac spinors and gamma5
26:37 - The vector (1/2, 1/2) irrep
35:18 - The bivector (1,0) and (0,1) irreps
45:30 - The rank-2 tensor (1,1) irrep
51:54 - Conclusion
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