 O(N)-invariant S-matrix

ID: o-n-invariant-s-matrix

For particles in the vector representation of the orthogonal group, the two-body S-matrix is a linear combination of the identity

I

P

and trace contraction

K

S = S_{2} I + S_{3} P + S_{1} K

. Here

K (e_{i} \otimes e_{j}) = δ_{ij} \sum_{a} e_{a} \otimes e_{a}

P^{2} = I

P K = K P = K

and

K^{2} = N K

. The orthogonal-invariant scattering channels diagonalize these three operators simultaneously.

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