Uploads from Richard Behiel

Currently Playing: The Strong Nuclear Force as a Gauge Theory, Part 2: Group Theory

Hey everyone, today we'll be talking about the group theory involved with quantum chromodynamics, not just SU(3) and su(3), but also U(N) and u(N) in general. This will give us the ideas and vocabulary we'll need, to explore how local SU(3) symmetry blossoms into the strong force. Along with this video, you can find the Video Notes PDF, and Animation Python codes, on my Patreon. Thank you to everyone who has signed up on there; your support means a lot and I really appreciate it! :) Patreon link: https://www.patreon.com/c/RichardBehiel 0:00 Intro, Transforming Triplet 11:42 Complex Vectors and Unitary Matrices 21:23 Group Theory, Definitions 30:18 Lie Group U(N), Lie Algebra u(N) 45:54 Special Unitary Group SU(N) 52:06 The Exponential Map 58:46 The su(3) Octopus 1:02:37 Topology of SU(3) 1:07:58 su(3) Structure Constants f^abc This video references two books, "Introduction to Elementary Particles" by David Griffiths, and "Gauge Theories of the Strong, Weak, and Electromagnetic Interactions" by Chris Quigg. While the video should stand on its own, so that it's not necessary to buy these books in order to follow along, the books offer a wealth of context and additional insight, so they're worth checking out. #physics #math #grouptheory #quantum #nuclear #chromodynamics