The Luttinger liquid model, proposed by Tomonaga and reformulated by J.M. Luttinger, describes electrons in one-dimensional electrical conductors under second-order interactions. Daniel C. Mattis [ de ] and Elliot H. Lieb proved in 1965 that electrons could be modeled as bosonic interactions. The response of the electron density to an external perturbation can be treated as plasmonic waves. This model predicts the emergence of spin–charge separation.