A quantum field theory of crystals. IV

One-dimensional boson and fermion systems are investigated for which the ground state expectation value of a molecule field does not exist; the assumptions on the energy bands and the two-body potential are the same for both systems. The systems behave essentially in the same fashion; they have particle-hole pairs, gapless phonons, energy dispersions with a linear momentum etc. It is shown that the coefficient of the momentum in the boson energy spectrum is larger than that in the fermion one.