Exact form factors of the O(N) $σ$-model

A general form factor formula for the $O(N)σ$-model is constructed and applied to several operators. The large N limits of these form factors are computed and compared with the 1/N expansion of the $O(N)σ$-model in terms of Feynman graphs and full agreement is found. In particular, O(3) and O(4) form factors are discussed. For the $O(3)σ$-model several low particle form factors are calculated explicitly.

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