Journal of Statistical Physics, Vol. 46, Nos. 3/4, 1987. p. 525-533.
A modification is given of Luttinger's one-dimensional model of interacting fermions to incorporate both Fermi surfaces using one physical type of particle. The system is solved in the presence of an arbitrary external field, with linear response and pair correlation functions readily computed. These constitute an explicit realization of a relation associated with the random phase approximation.