A quantum field theory of crystals and liquids

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 the atomic energy spectrum: the static elastic potential of the ground state and the vibrational free energy. The melting temperature is obtained by considering the free energy of the function of the gaps for the crystalline and liquid states.