please allow a question to 48:15 can U-dagger times U be 0 ? It's the same (real) vector. ( 1 0 ) or (0 1) - or in other words: can the dagger change the spin ?
In the end you mention the case of massless particles and that normalization is different. OK, but the U(p) also contains an "m" in the denominator. How do we handle that?
Confusion with the multiplication of gamma matrix with the p matrix- Isn't "p" a 4 vector? If that's the case, shouldn't one of p0 or p3 be negative? Thanks
We are multiplying gamma mu with the covariant p mu, which is (E,p0,p1,p2,p3), all positive. p mu contravariant is (E,p0,-p1,-p2,-p3). The gamma matrices were defined in this video, so you can see that no negative sign appears there. There would be a minus sign if we multiplied p mu with another 4-vector, but the gamma matrices are not a 4-vector. They are just 4 4x4 matrices
Best lecture series on QFT ever. You are so clear!!!!
I hope you always do these beautiful works and never stop because they are really very detailed!
Thank you for such an interesting explanation
please allow a question to 48:15
can U-dagger times U be 0 ? It's the same (real) vector. ( 1 0 ) or (0 1) - or in other words: can the dagger change the spin ?
Thank you ♡
Won't we write a general solution as superposition of the four states? And how did we interpret the basis as spin states?
In the end you mention the case of massless particles and that normalization is different. OK, but the U(p) also contains an "m" in the denominator. How do we handle that?
perfect!
Confusion with the multiplication of gamma matrix with the p matrix- Isn't "p" a 4 vector? If that's the case, shouldn't one of p0 or p3 be negative? Thanks
We are multiplying gamma mu with the covariant p mu, which is (E,p0,p1,p2,p3), all positive. p mu contravariant is (E,p0,-p1,-p2,-p3). The gamma matrices were defined in this video, so you can see that no negative sign appears there. There would be a minus sign if we multiplied p mu with another 4-vector, but the gamma matrices are not a 4-vector. They are just 4 4x4 matrices
@@NickHeumannUniversity Ah thanks for this, in your notation it looks like p has 5 components, were you saying that E=p0 for the first component?
@@chamelious oh, yes I just woke up lmao, p0 is E, I made a mistake, i wrote it twice
Why am i here while in high school💀