Uploads from Richard Behiel

Currently Playing: The Strong Nuclear Force as a Gauge Theory, Part 3: The Gluon Fields

Hey everyone, today we'll be deriving a gauge field, which will equip our lagrangian with local SU(3) symmetry. We'll go through each of the logical steps to prove that the four spacetime components of the gauge field must live in su(3), the Lie algebra of SU(3). Then, because G_mu lives in su(3), we'll see how we can write it in terms of eight real-valued four-vector fields, the gluon fields! 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, Dirac Lagrangian Does not have Local SU(3) Symmetry 7:15 Modifying the Lagrangian with D_mu 19:22 Deriving the Transformation Rule for G_mu 32:42 Showing that the new Lagrangian has Local SU(3) Symmetry 37:27 Exploring the Interaction Term, L_int 43:32 Why the Adjoint Transformation is a Thing 48:22 Proving that G_mu must be Hermitian 1:11:12 Shaving off the Traceful Part, so G_mu is in su(3) 1:19:27 The Gluon Fields 1:23:05 Our Model, so Far... 1:26:52 How to Bring G_mu to Life? 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