Exact formulas for the form factors of local operators in the Lieb-Liniger model

摘要: We present exact formulas for the form factors of local operators in repulsive Lieb-Liniger model at finite size. These are essential ingredients both numerical and analytical calculations. From theory Algebraic Bethe Ansatz, it is known that satisfy a particular type recursive relations. show some cases these relations can be used directly to derive compact expressions terms determinant matrix whose dimension scales linearly with system Our main results $(\Psi^{\dagger}(0))^2\Psi^2(0)$ $\Psi^{R}(0)$, arbitrary integer $R$, where $\Psi$, $\Psi^{\dagger}$ usual field operators. expressions, we also infinite size limit attractive regime.