Equation 14.81 in Zwiebach: Why No 2?

  • Thread starter Thread starter ehrenfest
  • Start date Start date
ehrenfest
Messages
2,001
Reaction score
1

Homework Statement


In equation 14.81, why are the lower indices of the oscillators alpha^r and alpha^s not divided by 2 like they were in equation 14.77?


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
ehrenfest said:

Homework Statement


In equation 14.81, why are the lower indices of the oscillators alpha^r and alpha^s not divided by 2 like they were in equation 14.77?


Homework Equations





The Attempt at a Solution


In my edition, equation 14.81 has no alpha (it has integrals with exponentials) . But my equation 14.82 has the commutator of alpha^r and alpha^s and they have, respectively, the subscripts m/2 and n/2.
I am not sure if you have that.
 
I'm sorry. I meant 14.80. Mine has subscripts of m and n (not divided by 2) so it must be a typo. That would make much more sense since the commutator of 14.82 in my book does have subscripts that are divided by 2.
 
Last edited:
I'm pretty sure it's a typo. Here is Professor Zwiebach's errata page. It has his e-mail address where you can send him this one.

http://xserver.lns.mit.edu/~zwiebach/firstcourse.html"
 
Last edited by a moderator:
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
Back
Top