We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density ${ \cal D}$. They are valid for all space and time and any interaction strength $c>0$, and are the leading order of an expansion in ${ \cal D}$. This expansion is obtained by writing the correlation functions as sums over form factors when formally decomposed into partial fractions.
Categories: math-ph cond-mat.quant-gas cond-mat.stat-mech math.MP