Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models
Abstract
We study the scalar product Sl,m between an on-shell and an off-shell Bethe state in models with SU(3)-invariance, where l and m denote the cardinalities of the two sets of Bethe roots. We construct recursion relations relating Sl,m to scalar products of smaller dimension, namely Sl-1,m and Sl,m-1. Solving these recursion relations we obtain new multiple integral expressions for Sl,m, whose integrands are (l+m) × (l+m) determinants, and closely related to the Slavnov determinant expression for the SU(2) scalar product.
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