= Two-pion isospin decomposition
{title2=$1\otimes1=2\oplus1\oplus0$}
Two <pions>, each of <isospin> one, have a nine-dimensional charge-state space. <Clebsch-Gordan coefficients> decompose it into an isospin-two quintet, an isospin-one triplet and an isospin-zero singlet. Under exchange of the two particle slots, the $I=2,0$ states are symmetric and the $I=1$ states are antisymmetric. Because <pions> have zero <spin> and obey <bosonic exchange symmetry>, the $I=1$ two-pion channel requires odd relative <orbital angular momentum>, while $I=0,2$ require even orbital angular momentum.
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