2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16607We summarize results on the asymptotics of the two-particle Green functions of interacting electrons in one dimension. Below a critical value of the chemical potential the Fermi surface vanishes, and the system can no longer be described as a Luttinger liquid. Instead, the non-relativistic Fermi gas with infinite point-like repulsion becomes the universal model for the long-wavelength, low temperature physics of the one-dimensional electrons. This model, which we call the impenetrable electron gas, allows for a rigorous mathematical treatment. In particular, a so-called determinant representation for the two particle Green function could be derived. This determinant representation is related to an integrable classical evolution equation and to a Riemann-Hilbert problem, that enable the exact calculation of the asymptotics of the two-particle Green functions.22 pages, AMS-Latex, invited talk, presented at the workshop on `Isomonodromic Deformations and Applications in Physics', Montreal, May 1-6, 2000Condensed MatterHigh Energy Physics - TheoryMathematical PhysicsExactly Solvable and Integrable Systemstext