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In this video, we explore the Higgs field, which has a nonzero expectation value throughout our universe, even in "empty" space. The Higgs field is very much like a superconducting condensate, and so we will use superconductivity as a way of exploring the Higgs field. The video begins with a crash course on superconductivity, then segues into an in-depth exploration of the Anderson-Higgs mechanism (in which gauge bosons acquire mass, by the consumption of Nambu-Goldstone modes), and finally we'll then explore the Higgs field in the context of the electroweak model. 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: / richardbehiel 0:00 Intro, We're Living in a Superconductor 14:15 Discovery, Onnes 21:03 Meissner Effect 25:27 London Eqs. 45:30 Type-II Superconductivity 55:16 Ginzburg-Landau Model 58:00 GL alpha, beta, and SSB 1:13:11 GL Kinetic and Magnetic Terms 1:17:39 GL Equations 1:22:09 Coherence Length 1:28:19 The Flux Quantum! 1:38:56 Flux Penetration 1:48:29 BCS Theory 1:54:11 Anderson-Higgs Overview 1:59:10 Nambu-Goldstone Modes 2:04:49 Helmholtz Decomposition 2:08:26 Local U(1) Transformation 2:14:16 Gauge-Covariant Derivative 2:21:39 Massive A in the U-Gauge 2:28:55 The Masochist Gauge 2:34:38 Transverse & Longitudinal Modes 2:40:32 Meissner, Revisited 2:43:11 Amplitude Mode in psi 2:45:04 SU(2) and U(1) 3:01:01 Four Forces 3:12:42 Electroweak Model 3:29:56 The Higgs Field 3:43:31 Higgs Mechanism 3:48:00 W Mass 3:56:57 Z Mass 4:03:51 U(1)_em 4:08:35 Gell-Mann Nishijima 4:22:47 Yukawa Couplings 4:26:27 The Higgs Boson! 4:41:42 What even is the Higgs Field?! 4:48:31 Vacuum Decay This video references three books, "Introduction to Elementary Particles" by David Griffiths, "Introduction to Superconductivity" by Michael Tinkham, 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. We also touch on a variety of papers throughout the video: "From Superconductors to Supercolliders", Lance Dixon (1996) https://tinyurl.com/bdzrtdut "On the Sudden Change in the Rate at which the Resistance of Mercury Disappears", Heike Kamerlingh Onnes (1911) https://tinyurl.com/y3mescm6 "Analysis of low-field isotropic vortex glass containing vortex groups in YBa2Cu3O7-x thin films visualized by scanning SQUID microscopy", Frederick S. Wells et al. (2015) https://tinyurl.com/9hvx3uhd "On the Theory of Superconductivity", V.L. Ginzburg, L.D. Landau (1950) https://tinyurl.com/dk7xvz8k "Theory of Superconductivity", J. Bardeen, L.N. Cooper, J.R. Schrieffer (1957) https://tinyurl.com/28266d32 "Microscopic Derivation of the Ginzburg-Landau Equations in the Theory of Superconductivity", L.P. Gor'kov (1959) https://tinyurl.com/bdd9cuz3 "Plasmons, Gauge Invariance, and Mass", P.W. Anderson (1963) https://tinyurl.com/3c43nfx8 "An introduction to spinors", Andrew M. Steane (2013) https://tinyurl.com/ednh429t "Broken Symmetries and the Masses of Gauge Bosons", Peter W. Higgs (1964) https://tinyurl.com/2mvj36xp "Electroweak Symmetry Breaking and the Higgs Boson", Antonio Pich (2015) https://tinyurl.com/2bjffma9 Hey, thanks again for checking out this video, I hope you learned something new! :) #physics #quantum #quantumphysics #superconductivity #maths #mathematics