Ryder, QFT, 1985, pg. 40, Eq. (2.69) K = sigma?

[Living_Dog]

Ryder, QFT, 1985, pg. 40, Eq. (2.69) K = sigma??

For the similar page in the 2nd edition, turn page 37 at this http://books.google.com/books?id=nn...resnum=1&ved=0CCwQ6wEwAA#v=onepage&q&f=false".

He states that K = +/- i/2 sigma.

How is this possible since the Pauli matrices are 2x2's and the K's are 4x4's. So ok, maybe he doubled up on the sigma's, but still, K_x != sigma_x, etc.

Thanks in advance.

 

[Fredrik]

37 and 38 aren't visible in the preview. There's no K on the pages I can see.

 

[matonski]

They are different K's. The 4x4 ones are the generators of boosts in spacetime. The 2x2 ones are the generators of boosts in spin 1/2 space. He most definitely did not double up on the sigmas here. He's just using the same letter since they are both generators of boosts.

 

[Living_Dog]

They are different K's. The 4x4 ones are the generators of boosts in spacetime. The 2x2 ones are the generators of boosts in spin 1/2 space. He most definitely did not double up on the sigmas here. He's just using the same letter since they are both generators of boosts.

Well then, what does this mean?

BTW, I moved on knowing how Ryder makes statements that are clear to him (and strong students) that leaves me in the dark. You know my previous post about the mystery with the $$\xi$$? It turns out that the way I described it in the end - as being utterly unnecessary - was correct. He dropped it in the 2^nd edition!

So this post is more in the way of a request to make the Ryder text less of a book on magic and more of a book on physics. (NOTE: texts are horrible teachers. They have no room for clearly EXPLAINING the material. I stopped buying books once I realized this. Now I pick one and struggle with it. Also PF is a very big help in this regard. So if no one has an answer then this bit of Ryder will remain in the dark... for me.)

I just checked the link. Page 37 is visible and the equation is at the bottom. Here is a snap of what I see:
http://img198.imageshack.us/img198/6726/ryder2edpg37.th.jpg

Uploaded with ImageShack.us

 

[Demystifier]

37 and 38 aren't visible in the preview. There's no K on the pages I can see.

Visibility (of free parts of a commercial book) strongly depends on where in the world your computer is.