I will report on a theoretical progress in understanding the spectral properties of one-dimensional quantum liquids. While for small energy and momentum transferred the spectral properties are explained (with notably exceptions) by the Luttinger model, their description at arbitrary energy/momentum remained an open problem until very recently. The situation changed in the last three years, and at present there exist several theories explaining the spectral properties of 1D systems
away from the Luttinger Liquid regime. I will discuss these theories and open questions.

LPTMS Orsay