A quantum field theory of crystals. II

A self-consistent treatment of one-dimensional crystals is presented by considering the Ward-Takahashi relations which stand for the spontaneous breakdown of the spatial translational invariance. It is shown that the boson condensations of the gapless phonons demonstrate how molecules arrange themselves in lattice structure so as to correspond to the two-body potential. For the delta-type potential, the lattice length vanishes and the system behaves like a superfluid system.