# Zwiebach page 197

1. Oct 22, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
I am confused about equation 11.58.
Doesn't that contradict equation 11.69 which should be -i by equation 11.58?

Is one of them using lc coordinates and the other one using the lc gauge? That is amazingly confusing for me if they are since they are not distinguished in any way?

2. Relevant equations

3. The attempt at a solution

2. Oct 23, 2007

### Jimmy Snyder

Actually, they are distinguished in the text. Above equation (11.58) it says:
while below equation (11.60) it says:
Then at the top of page 199, it says:
He might have added equation (11.69) to the list.

3. Oct 23, 2007

### ehrenfest

OK. So the commutation relation 11.58 is true only when those indices are 0,1,2,3 . I still think it is confusing that he uses the same greek letters mu and nu to represent Lorentz covariant coordinates and light-cone coordinates. When I go back to those equation I have no idea if they are true for lorentz coordinates, and/or lc coordinates, and/or the lc gauge.

Another thing that bothers me is that it seems like Zwiebach's only justification for 11.58 is that "it seems reasonable". We know it is true for the spatial part from QM, but how can you just write down an equation because it "seems reasonable"?

EDIT: wait. so apparently 11.58 is true for lc coordinates as he discusses in the paragraph underneath. in that case i just do not understand why it would not be true in the lc gauge because the lc gauge uses light cone coordinates and it is only a constraint on the lc coordinates so if 11.58 is true for lc coordinates shouldn't it be true for the constrained lc coordinates in the lc gauge?

Last edited: Oct 23, 2007
4. Oct 23, 2007

### ehrenfest

What am I missing? Is the lc gauge not a constraint like I am thinking of it?

Last edited: Oct 23, 2007
5. Oct 23, 2007

### ehrenfest

jimmy, i promise no more questions for 5 days if you answer this one :)

OK. So the commutation relation 11.58 is true only when those indices are 0,1,2,3 . I still think it is confusing that he uses the same greek letters mu and nu to represent Lorentz covariant coordinates and light-cone coordinates. When I go back to those equation I have no idea if they are true for lorentz coordinates, and/or lc coordinates, and/or the lc gauge.

Another thing that bothers me is that it seems like Zwiebach's only justification for 11.58 is that "it seems reasonable". We know it is true for the spatial part from QM, but how can you just write down an equation because it "seems reasonable"?

EDIT: wait. so apparently 11.58 is true for lc coordinates as he discusses in the paragraph underneath. in that case i just do not understand why it would not be true in the lc gauge because the lc gauge uses light cone coordinates and it is only a constraint on the lc coordinates so if 11.58 is true for lc coordinates shouldn't it be true for the constrained lc coordinates in the lc gauge?