The Density of States of the Tomonaga-Luttinger Model

The method of the boson representation is applied to the Tomonaga-Luttinger model to obtain the one-particle temperature Green's function which is derived by Dzyaloshinskii and Larkin. In case T=0, the method and the result are essentially same as those of Luther and Peshel. The density of states D(ω) is calculated in cases both T=0 and T≠0. It is shown that the quantity D(ω) near ω=0 is proportional to |ω|A in case T=0 and that the quantity D(0) at low temperatures is proportional to TA, where the quantity A is related to the strength of the interaction. A sum rule for D(ω) is derived.