Luttinger's model and the matter of dispersion

In the Luttinger model, right-hand-going particles moving at a constant vel ocity c in ID maintain a constant distance apart, Therefore their interacti on energy should be a trivial constant of the motion a whereas. in fact it is not. This interaction affects the dispersion of all the elementary excit ations in the model, hence the dynamics and thermodynamics. (Identical rema rks hold for the left-handgoers.) The present paper explores the meaning of this interesting Facet of Luttinger's model.