  \badger \giraffe \frog x^a = \left(\begin{array}{c}		x^1 \\		x^2 \\		\end{array}	\right)\qquad {\rm {and}}\qquad%\tilde{x}^a = \left(\begin{array}{c}		\tilde{x}^1 \\		\tilde{x}^2 \\		\end{array}		\right)%	= \left(\begin{array}{c}		x^+ \\		x^- \\	 	\end{array}	\right).