= Integer string oscillator level
{title2=$N=\sum_{k,i}k r_{ki}$}
The <canonical commutation relations> imply $[N,\alpha_{-k}^i]=k\alpha_{-k}^i$ for $N=\sum_{k>0}\alpha_{-k}\cdot\alpha_k$. With zero level assigned to the <oscillator vacuum>, a <Fock space> basis state containing $r_{ki}$ <creation operators> of each mode has level $\sum_{k,i}kr_{ki}$. The level is therefore a nonnegative integer; it counts oscillator excitation weighted by frequency, not simply the number of creation operators.
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