I really like the series.I new those math from a physiscist perspective and I am glad that now I am lesrning it from a mathematiciams.I also wanted to note that its called free boson algebra because this is the exact algebra used in the second quantization of a free real scalar(bosonic) field,and more perceisly in the creation of the Fock space of a free boson(with of curse some normilizations )
TLDR: thank you for your videos. I stopped at 7:30 because I have no idea what you're talking about; but I could tell you definitely know what you're talking about. You explain complex concepts concisely (I love that). I particularly enjoy how you organize and explain your organization of how these concepts come together. You've inspired me to learn a little more. I hope you teach something I can use.
fascinating to see this after having watched Leonard Susskind's "theoretical minimum" series, where he goes through the specifics of particle physics but without every mathematical detail. He treats creation and annihilation operators as abstract things that just behave a certain way, so its cool you hear you mention them as the result of all this set building stuff imma start from the start and try to understand it now lol
Awesome to see you top 100k. Well done. May I suggest when you have videos that connect to previous videos you provide links to previous videos so that we can catch up if we missed a pre-req?
Unrelated to my other post, is the answer to the homework 6a(-4)1? Also if I want to think about this in terms of partial derivatives is it 6d^2/(da(-3)da(-2)) (a(-4)a(-3)a(-2)1)?
I still don't understand the locality axiom. Multiplying by (z-w)^N shouldn't do anything, z and w even commute. What algebra of formal variables has zero divisors? And why should (z-w) be a zero divisor?
Here's a 1 variable example suggesting why it matters. z+z^2+z^3+... and -1/z - 1/z^2 - 1/z^3 - ... are clearly different series. But when we multiply both by 1-z, we get 1.
A = (3)(2)(-4)(-2)(-3)I -3 commutes with anything but 3 -2 commutes with anything but 2 A = (-4)(3)(-3)(2)(-2)I (2)(-2) = (-2)(2) + [2,-2] = (-2)(2) + 2k, and (2)I = 0, 2kI = 2I so A = (-4)(3)(-3) 2 I Similarly for (-3)(3) A = (-4) 3 * 2 * I = 6 (-4) I Hope someone tells me if I understood it right thank you
So if there are any string theorists that read this I'd love to know if I'm near the mark, or lost in the woods. There should be a Lie algebra which is the vector space H/DH. That lie algebra is where all the conserved quantities like the Hamiltonian live? There is an operator in H, alpha(-1) that is very much like a standard creation operator. You play commutation games to get rid of things that can't operate on the vacuum like in standard QM with density matrices. Where I'm really lost is as follows. There is not just one operator that can act on the vacuum, alpha of any negative integer can. There is also not only one operator that can't act on the vacuum, but any alpha of a positive integer can't. What do these other operators mean physically? What would a density matrix look like in this algebra? Finally is the translation operator like a super-translation?
@@evanev7Using the commutator I get α(-4)α(-2)α(2)α(-3)α(3) 1+2α(-4)α(-3)α(3)1+3α(-4)α(-2)α(2) 1+6α(-4) 1, but α(n)1=0 for n \geq 0 by definition, so only 6α(-4) 1 survives
i'm sorry but i'm already lost at 39sec in the video, even and odd vectors? Did i miss some videos required to understand those concepts please? I like math as a hobby and i enjoy this channel because it's kinda advanced but this is a bit too much for me i have to confess :D
I've watched every video you've ever made, and this is the first where I've no clue what you're talking about!
Huge congrats on 100k subscribers, it's really nice to see channels like yours grow!
congrats Michael, you are special
I really like the series.I new those math from a physiscist perspective and I am glad that now I am lesrning it from a mathematiciams.I also wanted to note that its called free boson algebra because this is the exact algebra used in the second quantization of a free real scalar(bosonic) field,and more perceisly in the creation of the Fock space of a free boson(with of curse some normilizations )
TLDR: thank you for your videos.
I stopped at 7:30 because I have no idea what you're talking about; but I could tell you definitely know what you're talking about. You explain complex concepts concisely (I love that). I particularly enjoy how you organize and explain your organization of how these concepts come together. You've inspired me to learn a little more. I hope you teach something I can use.
Thanks Prof Penn...thanks for another VOA video. .been looking forward to it after watching all of Sean Downes' videos on the Monster. .
100k congrats 🥳💐
Well done on reaching 100k you absolute wizzard!!!
Congratulations prof. Penn for 100k 🥳🥳🥳
Can’t wait to watch this whole series :)
Congratz on 100k my boy
Congrats on 100k
fascinating to see this after having watched Leonard Susskind's "theoretical minimum" series, where he goes through the specifics of particle physics but without every mathematical detail.
He treats creation and annihilation operators as abstract things that just behave a certain way, so its cool you hear you mention them as the result of all this set building stuff
imma start from the start and try to understand it now lol
Awesome to see you top 100k. Well done. May I suggest when you have videos that connect to previous videos you provide links to previous videos so that we can catch up if we missed a pre-req?
This is happening. I have a big project over winter break to do this type of bookkeeping.
Though the topic is difficult, it's not that hard to follow. Thank you for uploading!
很棒又有深度的 的教學
That “ok, great” T-shirt is awesome!
32:21
How is H=span{alpha(m1)....alpha(mk)} generated by (alpha(-1) acting on the vacuum vector)? I can see why {alpha(m)|m
Unrelated to my other post, is the answer to the homework 6a(-4)1? Also if I want to think about this in terms of partial derivatives is it 6d^2/(da(-3)da(-2)) (a(-4)a(-3)a(-2)1)?
21:01 you said m_k
I still don't understand the locality axiom. Multiplying by (z-w)^N shouldn't do anything, z and w even commute. What algebra of formal variables has zero divisors? And why should (z-w) be a zero divisor?
Here's a 1 variable example suggesting why it matters. z+z^2+z^3+... and -1/z - 1/z^2 - 1/z^3 - ... are clearly different series. But when we multiply both by 1-z, we get 1.
@@aadfg0 Interesting!
100k yay!
The title initially made me think of a Breaking Bad universe where Walter White teaches math instead of chemistry!
The reason Walter named himself Heisenberg is out of respect of the physicist.
A = (3)(2)(-4)(-2)(-3)I
-3 commutes with anything but 3
-2 commutes with anything but 2
A = (-4)(3)(-3)(2)(-2)I
(2)(-2) = (-2)(2) + [2,-2] = (-2)(2) + 2k, and (2)I = 0, 2kI = 2I so
A = (-4)(3)(-3) 2 I
Similarly for (-3)(3)
A = (-4) 3 * 2 * I = 6 (-4) I
Hope someone tells me if I understood it right thank you
So if there are any string theorists that read this I'd love to know if I'm near the mark, or lost in the woods. There should be a Lie algebra which is the vector space H/DH. That lie algebra is where all the conserved quantities like the Hamiltonian live? There is an operator in H, alpha(-1) that is very much like a standard creation operator. You play commutation games to get rid of things that can't operate on the vacuum like in standard QM with density matrices.
Where I'm really lost is as follows. There is not just one operator that can act on the vacuum, alpha of any negative integer can. There is also not only one operator that can't act on the vacuum, but any alpha of a positive integer can't. What do these other operators mean physically? What would a density matrix look like in this algebra? Finally is the translation operator like a super-translation?
how does the parity work in this algebra?
Good
For the HW:
α(3)α(2)α(-4)α(-2)α(-3)1 = α(-4)α(3)α(-3)α(2)α(-2)1 = α(-4)[α(-3)α(3) + α(-2)α(2) + 5k]1 = 5α(-4)1.
Hej, where does the 4k in the third expression come from? I get a 2k from α(2)α(-2) and a 3k from α(3)α(-3) and hence 6α(-4)1as result.
@@hyppie1234 Oh, I thought α(3)α(-3) gave you a 2k rather than a 3k.
@@hyppie1234 Looking back over it you're right it gives you a 3k, but that should bring the result to 5α(4)1, no?
@@evanev7Using the commutator I get α(-4)α(-2)α(2)α(-3)α(3) 1+2α(-4)α(-3)α(3)1+3α(-4)α(-2)α(2) 1+6α(-4) 1, but α(n)1=0 for n \geq 0 by definition, so only 6α(-4) 1 survives
@@hyppie1234 Yay that's what I got!
also Prove the Error Bound for Simpson's Rule
We all wanted a livesolve didnt we?
i'm sorry but i'm already lost at 39sec in the video, even and odd vectors? Did i miss some videos required to understand those concepts please?
I like math as a hobby and i enjoy this channel because it's kinda advanced but this is a bit too much for me i have to confess :D
100k subs!!! :D
¿Podrías activar los subtitulos en español?
I think maybe because this is a new video they haven't been generated yet. Check back later?
100k subscribers is a good place to stop.
dont.
Prove Cavalieri's Theorem
100k!!!!!!!!!
I just came here watching the word "heisenberg". As I am a Physics person.
WALTER WHITE : hold my beeer ... !
100k math olimpiad problems A ;G ; C ;N )))))))))))
I took 10 courses in math in college...and have no dam clue what he is talking about.
Lol this is measurement theory - Nice.