# Zwiebach QC 17.4, page 404

1. Nov 11, 2007

### Jimmy Snyder

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

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

3. The attempt at a solution
It seems easy: given |m> where w|m> = m|m> we have
$$w|e^{i\ell q_0/\~R}m> = e^{i\ell q_0/\~R}e^{-i\ell q_0/\~R}we^{i\ell q_0/\~R}|m> = e^{i\ell q_0/\~R}(w + \frac{\ell}{\~R})|m> = (m + \frac{\ell}{\~R})|e^{i\ell q_0/\~R}m>$$
So is there a typo in the book?

Last edited: Nov 11, 2007