Spinors for Beginners 16: Lie Groups and Lie Algebras

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 Videos on momentum operator generating translations in quantum mechanics: Physics with Elliot: https://www.youtube.com/watch?v=_lz1VfI6Wxk&t=596s&pp=ygUecGh5c2ljcyB3aXRoIGVsbGlvdCBjb21tdXRhdG9y Professor M Does Science's video: https://www.youtube.com/watch?v=978mMgGYs1M&t=392s&pp=ygUkcHJvZmVzc29yIG0gZG9lcyBzY2llbmNlIHRyYW5zbGF0aW9u Quantum Sense': https://www.youtube.com/watch?v=A7yDvA8VQC8&t=305s&pp=ygUZcXVhbnR1bSBzZW5zZSB0cmFuc2xhdGlvbg%3D%3D 0:00 - Introduction 2:45 - Groups & Lie Groups 4:00 - Exponent of a so(3) Matrix 7:40 - Calculating so(3) generators 9:50 - Momentum generators translations 10:58 - so(3) traceless proof 13:35 - so(3) anti-symmetric proof 15:11 - Warning about matrix exponentials 16:43 - Lie Algebra Bracket 20:24 - Structure coefficients 21:48 - Lie Algebras as Tangent Spaces 23:30 - Lie Algebra Property Proofs 30:15 - Summary of so(3) 31:05 - Overview of so+(1,3) 32:50 - Spin-1 and Spin-1/2 representations 34:40 - Math vs Physics conventions