Electromagnetism as a Gauge Theory

Video Description

"Why is electromagnetism a thing?" That's the question. In this video, we explore the answer given by gauge theory. In a nutshell, electromagnetism arises from local phase symmetry. But what does that mean, and how exactly does that work? That's what this video is all about! :) Video notes PDF and python animation codes are on patreon: https://www.patreon.com/RichardBehiel *This video is quite long and technical.* Think of it as a video textbook, so you can skip around to different parts if you’d like. But I wanted to err on the side of rigor and thoroughness, to show comprehensively how local U(1) symmetry blossoms into electromagnetism. So the ideas are all there for you, but you don’t have to watch this in one sitting! 😅 This video frequently references "Introduction to Elementary Particles" by David Griffiths, which is one of the greatest textbooks of all time. Highly recommend checking it out or buying a copy. Also, see "An introduction to spinors" by Andrew M. Steane, for an explanation of how the spinor flag diagram works: https://arxiv.org/pdf/1312.3824 See also the famous YouTube series "Spinors for Beginners" by eigenchris, for more information about spinors. Shoutout to Curt Jaimungal for introducing me to the spinor flag diagram, and for the video editing advice! Check out his YouTube channel, Theories of Everything: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w Chapters: 0:00 Intro - "Why is Electromagnetism a Thing?" 14:24 Dirac Zero-Momentum Eigenstates 39:10 Local Phase Symmetry 52:07 A Curious Lagrangian 1:11:43 Bringing A to Life, in Six Ways 1:27:40 The Homogeneous Maxwell's Equations 1:39:25 The Faraday Tensor 1:47:49 F_munuF^munu 1:53:05 The Lagrangian of Quantum Electrodynamics 1:58:14 Inhomogeneous Maxwell's Equations, Part 1 2:11:07 ... Part 2, Solving Euler-Lagrange 2:31:10 ... Part 3, Unpacking the Inhomogeneous Maxwell's Equation(s) 2:37:55 Local Charge Conservation 2:42:20 Deriving the Lorentz Force Law 3:01:25 Miscellaneous Stuff & Mysteries #math #physics #quantum #relativity #electromagnetism