Spinors for Beginners 16: Lie Groups and Lie Algebras

Full spinors playlist: Leave me a tip: Powerpoint slide files Exercise answers: Videos on momentum operator generating translations in quantum mechanics: Physics with Elliot: Professor M Does Science’s video: Quantum Sense’: 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