On Form Factors of the conjugated field in the non-linear Schröodinger model

Details On Form Factors of the conjugated field in the non-linear Schröodinger model On Form Factors of the conjugated field in the non-linear Schröodinger model

2011-05-05

arxiv.org/abs/1105.1052v1

Physics

Mathematical Physics

23 pages

Scientific paper

Izergin-Korepin's lattice discretization of the non-linear Schr\"odinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic parameters.

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