Thanks a lot for your videos. I'm self learning these things and you are helping me so much. Please don't stop uploading new videos. Your effort is much appreciated 😊
The motivation to formulate the Lorentz matrix in terms of hyperbolic cosh and sinh seems to be it being analogously to ordinary rotation matrices. But the job could be done in terms of gamma and betha also, right? I formulated a Lorentz Tr. in still other terms after playing around a little. My inverse tr. matrix (primed to unprimed) unfortunately has a (positive) huge det far beyond 1 ( bec. a scalar multiplication is involved), but leads to the correct solution of t and x nevertheless. The first way matrix (unprimed to primed) has a det =1. Could you comment why that would be rejected and regarded as a „unproper“ transformation? Why does the det matter so much? I mean „gamma^2 minus (betha*gamma)^2 = 1“ is preserved first way but not backwards, giving the correct result though, to repeat the Q in more technical terms! Vielen Dank im Voraus und sehr ansprechend gemacht - den gewöhnungsbedürftigen Stoff! 55:52
This playlist is god sent to save me!! btw what do you mean by one matrix commuting with the other, my professor also keeps saying that, I don't exactly understand what it means. Thank you so much for this amazing videos.
if we have matrix A and matrix B, we say that they commute if [A,B]=A*B-B*A=0, in other terms, A*B=B*A. The bracket terms is called the "commutator of A and B"
@@artpegios OK I was gonna ask you for some help? I’m in my 40s and not going to school. I just have an interest in this and have spent the last several years studying QFT and maybe making some progress?
Is it correct to contract the second index of eta with the second index of epsilon, like what u did in 34:00 ? As long as we contract one top and one bottom, it doesn't matter which index of eta gets contracted with which index of epsilon? Is that right? Because we all so used to seeing only 2nd index of the first variable contracting with the first index of the second variable.
Dirac and Lorentz Transformations Dirac took an electron and figured out how the electron will transform under the Lorentz transformations and after published the results as the existence of an antielectron / positron. Electron after Lorentz transformations changes into an antielectron.
The inverse and transpose are the same in this case because of the fact that the lorentz transformation matrix we used is orthogonal (as I proved in the video). So it doesn't matter whether you call it inverse or transpose, beyond the emphasis that you want to make
exercise set: 1. (a) write down the rotation matrix in 3D. (b) show that this matrix is orthogonal. (c) show that det R (from b) = 1 (d) Derive the infinitesimal rotation generator from it. 2. (a) show that Lorentz transformation is orthogonal. (b) calculate the infinitesimal Lorentz transformation. (c) calculate the det. of the Lorentz matrix. (d) derive the Lorentz invariant quantity and show with an example that it works pretty well.
@@NickHeumannUniversity Thank you. I am going through it. Also there is the concept of J mu in the lecture, titled, "Noether's Theorem and the Momentum of the Klein-Gordon Field". I will also go through it. I hope both the J mu s are the same.
![เปิดบ้าน นาราเครปกระเทย 1 ไร่ ขายขาดทุนหลัก10ล้าน เอามาใช้หนี้!!! l [Nickynachat]](http://i.ytimg.com/vi/0jz84VFWVP4/mqdefault.jpg)
Thanks a lot for your videos. I'm self learning these things and you are helping me so much. Please don't stop uploading new videos. Your effort is much appreciated 😊
wonderful. simply wonderful
The motivation to formulate the Lorentz matrix in terms of hyperbolic cosh and sinh seems to be it being analogously to ordinary rotation matrices. But the job could be done in terms of gamma and betha also, right? I formulated a Lorentz Tr. in still other terms after playing around a little. My inverse tr. matrix (primed to unprimed) unfortunately has a (positive) huge det far beyond 1 ( bec. a scalar multiplication is involved), but leads to the correct solution of t and x nevertheless. The first way matrix (unprimed to primed) has a det =1. Could you comment why that would be rejected and regarded as a „unproper“ transformation? Why does the det matter so much? I mean „gamma^2 minus (betha*gamma)^2 = 1“ is preserved first way but not backwards, giving the correct result though, to repeat the Q in more technical terms! Vielen Dank im Voraus und sehr ansprechend gemacht - den gewöhnungsbedürftigen Stoff! 55:52
Refference please
Excellent presentation
This playlist is god sent to save me!! btw what do you mean by one matrix commuting with the other, my professor also keeps saying that, I don't exactly understand what it means. Thank you so much for this amazing videos.
if we have matrix A and matrix B, we say that they commute if [A,B]=A*B-B*A=0, in other terms, A*B=B*A. The bracket terms is called the "commutator of A and B"
Ahh okay, I get it now. I guess it means we can change their order i.e. B*A since they commute. Thank you so much!
you made my day sir, wish i understood more Spanish so i could watch your other channel
does he have a Spanish channel :0?
@@artpegios He does, but I do not think he has Spanish for QFT
@@artpegios do you teach?
@@JoeHynes284 undergrad student 😅
@@artpegios OK I was gonna ask you for some help? I’m in my 40s and not going to school. I just have an interest in this and have spent the last several years studying QFT and maybe making some progress?
Thank you Brother Nick. When referring to the delta symbol, you kept saying Dirac delta symbol. I think you meant Kronecker delta symbol.
Is it correct to contract the second index of eta with the second index of epsilon, like what u did in 34:00 ? As long as we contract one top and one bottom, it doesn't matter which index of eta gets contracted with which index of epsilon? Is that right?
Because we all so used to seeing only 2nd index of the first variable contracting with the first index of the second variable.
Dirac and Lorentz Transformations
Dirac took an electron and figured out how the electron will transform
under the Lorentz transformations and after published the results
as the existence of an antielectron / positron.
Electron after Lorentz transformations changes into an antielectron.
thank you for your videos :D can i ask which book did you used for this topic? tyyy
Minute 24
Would it be better to use the definition INVERSE instead of TRANSPOSE?
The inverse and transpose are the same in this case because of the fact that the lorentz transformation matrix we used is orthogonal (as I proved in the video). So it doesn't matter whether you call it inverse or transpose, beyond the emphasis that you want to make
exercise set:
1. (a) write down the rotation matrix in 3D.
(b) show that this matrix is orthogonal.
(c) show that det R (from b) = 1
(d) Derive the infinitesimal rotation generator from it.
2. (a) show that Lorentz transformation is orthogonal.
(b) calculate the infinitesimal Lorentz transformation.
(c) calculate the det. of the Lorentz matrix.
(d) derive the Lorentz invariant quantity and show with an example that it works pretty well.
Note : I just dropped this comment so that I can come here later on and check my own comprehension before exam or nothing special.
Thanks a lot for the lectures. In which lecture can I know about the current J mu, conserved charge ? Thank you
it is in this lecture, number 5, around 40 minutes:
th-cam.com/video/0oa-srfXmxk/w-d-xo.html
@@NickHeumannUniversity Thank you. I am going through it. Also there is the concept of J mu in the lecture, titled, "Noether's Theorem and the Momentum of the Klein-Gordon Field". I will also go through it. I hope both the J mu s are the same.
it's the vector, not the coordinates that is rotated, isn't it?
40:11 wow❤