  $$\begin{split} & \left\lbrace  \psi^{i}, \psi^{j}   \right\rbrace= \left\lbrace  \psi_{i}, \psi_{j} \right\rbrace = 0  \\ & \left\lbrace  \psi^{i}, \psi_{j}   \right\rbrace= \delta^{i}_{j}. \end{split}$$  