\left\langle S_{z}\right\rangle _{-}=\langle \overline{z}_{-}\overline{z}%_{-}\Psi ^{--}\left( x;\tau \right) \left| \frac{1}{2}\left( \overline{z}_{+}%\frac{\partial }{\partial \overline{z}_{+}}-\overline{z}_{-}\frac{\partial }{%\partial \overline{z}_{-}}\right) \right|  \tiger\seahorse \deer\pigeon\walrus