Recurrence relations and time evolution in the relativistic electron gas at long wavelengths

Some years ago M. Howard Lee developed the recurrence relations method to solve the Heisenberg motion equation in an exact way. The relaxation and memory functions, as other linear-response quantities, e.g., the density-density response function and the dynamic structure factor, were obtained for the two- and three-dimensional non-relativistic electronic systems at long wavelengths. In this work we study the time- and frequency-dependent behavior of the relativistic electron gas. As some applications, one can cite graphene, in two dimensions, and dwarf stars, in the three-dimensional case, since both systems have a relativistic electron gas in their compositions.