A quantum field-theoretical treatment of crystals is presented from the view-point of the spontaneous break-down of the spatial translational invariance. Our treatment starts with the assumption of the existence of the ground-state expectation value of a molecule field. It is proved that there...

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...

A two-band model is considered in one-dimensional fermion systems. The particle-hole pairs are favourable for our symmetry bands and the positive value of the two-body potential. The boson condensations of the particle-hole pairs are expected to form crystals. The gapless boson spectrum is shown...

A quantum field theoretical treatment of three-dimensional cubic crystals at finite temperature is presented from the view-point of the spontaneous breakdown of the spatial translational invariance using thermo field theory. The effective interaction Hamiltonian is constructed by taking into...

Phonons and boiling in liquids is investigated from the viewpoint of quantum field theory at finite temperature, starting with atoms interacting with each other as the first principle. The Ward-Takahashi relation associated with the spontaneous breakdown of the translational invariance in the...

The free energy and thermodynamical properties for the crystalline and liquid states are calculated from the viewpoint of quantum field theory similar to superconductivity and magnetism including all the couplings of the density fluctuations. The free energy consists of a function of the gaps of...

Atom and phonon Green functions are determined by the Ward-Takahashi relations associated with the spatially translational and rotational invariance. In the random phase approximation, the energy spectrum of atoms is constructed by introducing the hopping to atoms in their own harmonic...

Atom and phonon Green's functions and a gap equation of atoms are derived from the viewpoint of the spontaneous breakdown of symmetry, considering the two concrete Ward-Takahashi relations represented by atom and phonon Green's functions, taking into account all the couplings between the density...

The effective interaction Hamiltonian in 3D nonlinear lattices is established taking into account the repetitions of the up and down transition of an atom between two levels at the same site. The effective interaction Hamiltonian leads to the Heisenberg equation for phonon operators, which...

The free energy for the crystalline state and the liquid state is investigated at low temperatures and near the melting temperature from a quantum field theoretical point of view, starting with atoms interacting with each other. The order parameter is defined by the energy gaps on the Brillouin...