Mean field theory and boson expansion at finite temperature on the basis of the thermo field dynamics

Abstract

Thermo field dynamics (TFD) is applied to the general hamiltonian with two-body interaction. The Hartree-Fock-Bogoliubov (HFB) equation and RPA at finite temperature are derived by the approximate diagonalization of the time translational operator of TFD. A boson expansion theory at finite temperature is developed by introducing duplicated boson spaces as the image of the boson mapping. These methods are applied to the two-level Lipkin model in which the basic group is shown to become O(5) at finite temperature in place of SU(2).