When typos or other errors are found in the problem sets, the problem sets on the course web page will be updated, and the changes noted here.
Problem 1. As was probably clear from the rest of the problem, the first sentence should read: ``Let S denote the frame of the station platform and S' the frame moving with the train at velocity v.'' (The prime was missing on the second S.)
The instructions should read, ``Please do problems 1 and 2. For problems 3-6, pick any two or do more than two for extra credit.'' (The second sentence originally said 4-6 instead of 3-6.)
Problem 1. In the first equation, the indices of g should be mu nu. (Originally, they were m n.)
Problem 1. Added the following explanatory sentence after ``where commas denote partial differentiation'':
I.e., h_{alpha nu, beta} = partial_{beta} h_{alpha nu} and h_{alpha nu, beta mu} = partial_{mu} (h_{alpha nu, beta}) = partial_{mu} partial_{beta} h_{alpha nu}.
Problem 1. Added the following after the matrices for F and L: ``where in the second equation we have specialized to the case of a Lorentz boost in the x^3 direction.''
Problem 1. Added the following hint to part (a)(iii):
[Hint: for this part, and for part (b)(iii), you might find it easiest to first show that the action of a Lorentz boost on F^{mu nu} can be written in terms of the electric and magnetic fields as
E'_\parallel = E_\parallel,
E'_\perp = gamma (E_\perp+(v/c)×B),
B'_\parallel = B_\parallel,
B'_\perp = gamma (B_\perp-(v/c)×E),
where \parallel and \perp denote components parallel and perpendicular to v, respectively.]
Note: This hint above was wrong as it originally appeared. The second E and B on the right hand side of the equations for perpendicular components were accidentally interchanged. Whoever pointed this out by anonymous feedback -- thanks!
Problem 1. There was a significant error in the original formulation of this problem. In short, there are two nonzero critical values of the radius, not one. Please see the new version for corrections and clarifications. Because of this error, the problem set will now be graded on the basis of three problems for full credit rather than four. Problem 1 is now extra credit. The deadline for submitting a solution to Problem 1 has been extended for one week.
Problem 2. Added the following sentence: ``For this problem, you will need the result of Problem 5 on the last problem set (Zwiebach Problem 8.7), which in the point particle context states that if there exists a symmetry such that
delta L = [d/d(tau)] (epsilon^i(tau) Lambda_i),
then the corresponding conserved charges Q_i are given by
epsilon^i Q_i = [d L/d(d_{tau} x^{mu})] delta x^{mu} - epsilon^i Lambda_i.''
Problem 1. In Eq. (2), the numerical factor on the right hand side is -1/(2 pi)^2, not -2/pi as originally stated.
Problem 3. There were minor changes to the background information, with no change to the problem itself.
Problem 4. Added an assumption of an intermediate result that makes the problem more tractable. See updated pdf file.
Problem 4. Zwiebach Eq. (12.162) seems to be off by a minus sign. The problem has been updated to indicate this.
In the Step 1 paragraph on p.2:
Added ``The position of alpha_0 is unimportant since alpha_0 commutes with L^\perp_n and alpha_n.'' Changed m,n>0 to m,n>=0 in Eq. (16).