CONDUCTIVITY OF A LUTTINGER LIQUID

We show that the real part of the frequency-dependent conductivity of interacting spinless fermions at incommensurate band fillings in one dimension at T = 0 is proportional to omega3 for small positive frequencies, contrary to statements in the recent literature. We argue that the de conductivity of spinless fermions at incommensurate band fillings diverges faster than any power of 1/T as T --> 0. We give the extension of our results to the case of commensurate band fillings and fermions with spin.