Zwiebach Exercise 9.3b: Solving for 4a in Equation 9.10

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Homework Help Overview

The discussion revolves around a problem from string theory, specifically related to Zwiebach's Exercise 9.3b, which involves interpreting Equation 9.10 and determining the correct expression for a variable denoted as 4a.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of Equation 9.10, questioning whether the coefficient of 4a should be interpreted differently. There is mention of integrating differential lengths over specific ranges, with some confusion about the context of closed versus open strings.

Discussion Status

The discussion is ongoing, with participants sharing their interpretations and clarifications about the problem. Some guidance has been offered regarding the integration process, but there is no explicit consensus on the interpretation of the equation or the correct form of the answer.

Contextual Notes

There is a noted distinction between closed and open strings in the context of the problem, which may affect the interpretation of the integration limits and the resulting expressions.

ehrenfest
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Homework Statement


Apparently the answer is sqrt(2 alpha') *4a. But doesn't equation 9.10 imply that the 4a should just be a 1?


Homework Equations





The Attempt at a Solution

 
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It's kind of a coincidence that when I did that problem two years ago, that's what I wrote in the margin of my book. However it is not true. [itex]l_s[/itex] is just a unit of length like the Planck length. It is not necessarily the length of any string. It is useful as a unit of length when doing string theory as this problem shows. The answer is [itex]4\sqrt{2}a[/itex] in units of the string length.
 
Last edited:
I see--we need to integrate differential lengths from sigma = 0 to sigma = 2 pi. Thanks.
 
Last edited:
ehrenfest said:
I see--we need to integrate differential lengths from sigma = 0 to sigma = 2 pi. Thanks.
That's for closed strings. As this is an open string, the range is different.
 

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