2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101610Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in 1/γwhere γis Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-γregime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak p-wave interactions as well as for strongly interacting bosons.13 pages, 5 figures, the journal versionStatistical MechanicsMathematical Physicstext