Ground State Energy of the One-Dimensional Electron System with Short-Range Interaction. I

The ground state energy of the one-dimensional electron gas interacting via a delta-function potential is considered as a function of interaction (c) for the given magnetization. The integral equations of Gaudin and Yang are used. It is shown that the ground state energy can be analytically continued at c = 0 for non-zero magnetization. This fact holds also for the one-dimensional Hubbard model except for the half-filled case.