Formula_756

\[\left.\begin{array}{l}\left\langle O, \tilde{a}_{k}\right\rangle_{t}=N_{k}\left\langle\left[\tilde{a}_{k}, O\right]\right\rangle_{t}, \\\left\langle\tilde{a}_{k}, O\right\rangle_{t}=\left(1+N_{k}\right)\left\langle\left[\tilde{a}_{k}, O\right]\right\rangle_{t},\end{array}\right\}\]