Thirring fermions at high temperature

A Green's-function method is used to study the thermodynamic properties of self-interacting massless fermions in one space dimension and one time dimension. It is shown that the exact expression can be obtained for the thermodynamic one-particle Green's function for the case where the dimensionless chemical potential $\mu =0\mathrm{}$, which is identical with the corresponding field-theoretic Green's function. The number density is obtained as an infinite sum. It exhibits a peculiar peaked behavior as a function of momentum. The energy, however, is a continuous function of temperature.