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Exact form factors of the \(O(N)\) \(\sigma\)-model. (English) Zbl 1342.81151

Summary: A general form factor formula for the \(O(N)\) \(\sigma\)-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 \(O(N)\) \(\sigma\)-model in terms of Feynman graphs and full agreement is found. In particular, \(O(3)\) and \(O(4)\) form factors are discussed. For the \(O(3)\) \(\sigma\)-model several low particle form factors are calculated explicitly.

MSC:

81Q40 Bethe-Salpeter and other integral equations arising in quantum theory
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