Quantum Invariance & The Origin of The Standard Model
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it when explaining quantum phase, U(1) local phase transformations and gauge invariance, and how electromagnetism emerges from them.
Recommended by 2 people across 2 different months, 2018 to 2022.
What it is
A PBS Space Time episode hosted by Matt O'Dowd on gauge theory and quantum invariance, showing how symmetries of the equations of motion, such as local phase invariance and U(1), lead to the structure of the Standard Model. It builds on the idea that symmetries imply conserved quantities and goes further to predict new physics.
What people said
Recommends Marc DiNino · 2018-10 · Physics Stack Exchange · on “Does a moving electrically charged particle have a "magnetic charge"?”
I really liked this MinutePhysics video that talks about the relationship between relativity and electromagnetism. [LINK] This PBS SpaceTime video goes into more depth and touches on how it relates to quantum invariance [this video] I can't point you to precise equations but electric and magnetic charge are two sides of the same coin and can't be pulled apart. One is simply the other in a difference reference frame. This is another good video [LINK] . I actually bought a Lentz tube off of Amazon so I can see this is person. So cool.
Recommends Tfovid · 2020-08 · Physics Stack Exchange · on “Can someone provide a physical -- not mathematical -- intuition for the phase in a quantum wavefunction?”
@QuantumFumbler The first part of this video touches on the notion of quantum phase and its relation to the complexity of the wave function: [ [this video] ] . The visualization of minute 4:21 was somewhat of an aha-moment for me as well.
Cites Liam Clink · 2018-11 · Physics Stack Exchange · on “Wave group and phase velocities”
Phase velocity and group velocity are determined by the dispersion relation, which is typically the angular frequency as a function of wavenumber: $\omega(k)$ . The dispersion relation can be measured and used to infer properties of the wave and its medium; this is a very common thing to do in Condensed Matter physics. A wonderfully complex example of this is explored in this question: What information can we extract from the electronic band structure? [LINK] Because they don't teach this in chemistry or basic physics courses usually, it's likely that you didn't even know that band structure IS a dispersion relation. It is the dispersion relation for electrons in a crystal of that material.
Cites Lisastronomy · 2022-12 · Physics Stack Exchange · on “Schrödinger equation and $\rm U(1)$ group”
I watched two youtube videos: [LINK] and [this video] . Now, I compared those two videos. One talk about the breaking of the Schrödinger equation after applying local phase transformations, and the other talks about the Lagrangian. My question is, is it right to talk about the breaking in the Schrödinger equation, the same way as the symmetry breaking in the Lagrangian, by applying a $\rm U(1)$ group? So can you apply $\rm U(1)$ to the Schrödinger equation, and say that is the local phase transformation? I am sorry if this an easy question. For background information: I am a first year student doing a project about quantum field theory for a video.