Im working through derivations of string equations of motion from the Nambu-Goto Action and I'm stuck on something that I think must be trivial, just a math step that I cant really see how to work through.(adsbygoogle = window.adsbygoogle || []).push({});

At this point Ive derived the equation of motion for the closed string from the wave equation in a general [tex] \tau [/tex] gauge, and now im trying to do the same but for a string in space with compactified dimensions. So im trying to implement

[tex] X^i (\tau, \sigma) = X^i (\tau , \sigma +2\pi) +2\pi R_i W^i [/tex]

Where W is wrapping number of ther string around the dimension.

Now, without the compactified dimension it was simple to see the periodicity of the left moving wave and the right moving wave separately, and to expand using fourier expansion and combine the 2 to get the equation of motion. But now im stuck on how to use the constraint to again rederive the equation of motion from the general solution to the wave equation. how do you do the mode expansion now that you have this extra term of

[tex] 2\pi R_i W^i[/tex] ?

Thanks for any help.

B

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# Mode Expansion of Closed String with Compact Dimensions

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