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Zwiebach QC 17.4, page 404

  1. Nov 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Verify that acting on a state with winding m, the operator
    [tex]e^{i\ell q_0/\~R}[/tex]
    gives a state with winding [itex]m + \ell[/itex]

    2. Relevant equations
    Equation (17.83)
    [tex]e^{-i\ell q_0/\~R}we^{i\ell q_0/\~R} = w + \frac{\ell}{\~R}[/tex]

    3. The attempt at a solution
    It seems easy: given |m> where w|m> = m|m> we have
    [tex]w|e^{i\ell q_0/\~R}m> = e^{i\ell q_0/\~R}e^{-i\ell q_0/\~R}we^{i\ell q_0/\~R}|m> = e^{i\ell q_0/\~R}(w + \frac{\ell}{\~R})|m> = (m + \frac{\ell}{\~R})|e^{i\ell q_0/\~R}m>[/tex]
    So is there a typo in the book?
    Last edited: Nov 11, 2007
  2. jcsd
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