IKR?! I feel like I've been waiting forever for a return to the higher math lectures, so today being BOGO was awesome 😁 I wish he/Justin still did the example videos, I would really like to follow along with them for more advanced topics like this, concrete examples would really illustrate what's going on in the lectures imo.
Awesome lecture as always!! A few comments... 1)is there anywhere else (such as an unrestricted university website) that you're hosting these videos instead of CZcams? With their ad policies getting more and more insane, I fear I will lose access to a lot of the educational content that got me where I currently am... 2)I would love to see worked example videos again for these higher level courses! With more advanced topics, following along with example problems feels more like illustrating symmetry/art than just running drills. I hope Justin is okay, too! 3)on a more video specific note, I would really like to see you go into detail on the Hilbert space representation of the Heisenberg group/algebra!!!!!!!!!!!! The wiki for Fock Space is very focused on the physics, Stone von Neumann thm is a bit too abstract for an introduction, and there's a half dozen vaguely related wiki pages on Theta Representation vs Oscillator Representation vs Schroedinger Representation etc that almost illustrate what you're talking about but are harder to navigate and piece together... but I find your videos extremely intuitive, and an explainer would help a lot (especially since the nil Thurston geometry makes the Heisenberg group one of my favorite manifolds haha)
You stated the kronecker delta the other way round: it is 0 when its subindexes are different and equal to 1 otherwise. In the example of the heisenberg Lie Algebra you have assumed it correctly though.
a return to differential forms AND a new lie algebras video? everything’s coming up milhouse!
IKR?! I feel like I've been waiting forever for a return to the higher math lectures, so today being BOGO was awesome 😁 I wish he/Justin still did the example videos, I would really like to follow along with them for more advanced topics like this, concrete examples would really illustrate what's going on in the lectures imo.
Awesome lecture as always!! A few comments...
1)is there anywhere else (such as an unrestricted university website) that you're hosting these videos instead of CZcams? With their ad policies getting more and more insane, I fear I will lose access to a lot of the educational content that got me where I currently am...
2)I would love to see worked example videos again for these higher level courses! With more advanced topics, following along with example problems feels more like illustrating symmetry/art than just running drills. I hope Justin is okay, too!
3)on a more video specific note, I would really like to see you go into detail on the Hilbert space representation of the Heisenberg group/algebra!!!!!!!!!!!! The wiki for Fock Space is very focused on the physics, Stone von Neumann thm is a bit too abstract for an introduction, and there's a half dozen vaguely related wiki pages on Theta Representation vs Oscillator Representation vs Schroedinger Representation etc that almost illustrate what you're talking about but are harder to navigate and piece together... but I find your videos extremely intuitive, and an explainer would help a lot (especially since the nil Thurston geometry makes the Heisenberg group one of my favorite manifolds haha)
You stated the kronecker delta the other way round: it is 0 when its subindexes are different and equal to 1 otherwise. In the example of the heisenberg Lie Algebra you have assumed it correctly though.