= SU(2)-invariant antisymmetric spinor contraction
{c}
{title2=$\phi^T\varepsilon\chi$}
For $\varepsilon=\begin{pmatrix}0&1\\-1&0\end{pmatrix}$, every two-by-two matrix satisfies $U^T\varepsilon U=(\det U)\varepsilon$. Thus $\phi^T\varepsilon\chi$ is exactly invariant under a common <SU(2) group> transformation. This is a bilinear contraction without <complex conjugation>. It vanishes for equal commuting <spinors> and is the alternating tensor defining the <spin singlet state>. Overall bosonic exchange symmetry must still be enforced if the <spinors> label identical particles.
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