Spinors for Beginners 16: Lie Groups and Lie Algebras
Автор: eigenchris
Загружено: 2023-12-10
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Videos on momentum operator generating translations in quantum mechanics:
Physics with Elliot: • The Symmetry at the Heart of the Canonical...
Professor M Does Science's video: • The translation operator in quantum mechanics
Quantum Sense': • Ch 14: Where does the momentum operator co...
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
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