The repulsive Lieb-Liniger model can be obtained as the non-relativistic
limit of the Sinh-Gordon model: all physical quantities of the latter model
(S-matrix, Lagrangian and operators) can be put in correspondence with those of
the former. We use this mapping, together with the Thermodynamical Bethe Ansatz
equations and the exact form factors of the Sinh-Gordon model, to set up a
compact and general formalism for computing the expectation values of the
Lieb-Liniger model both at zero and finite temperature. The computation of
one-point correlators is thoroughly detailed and, when possible, compared with
known results in the literature.Comment: published version, 27 pages, 10 figure
