Exchange energy and specific heat of the electron gas at low temperature

By the closed-path Green's function approach an explicit expression of the thermodynamic potential with a new form of the exchange term of the electron gas is derived. It is shown that at finite temperature this exchange term can be reduced to the conventional one resulting from the imaginary-time Green's function formalism, but at low temperature, contrary to the latter, is free from the T ln T trouble. Starting from this thermodynamic potential the specific heat of the electron gas at low temperature is calculated within the range of electron densities of metals. (C) 2001 Elsevier Science B.V. All rights reserved,