A quantum field theory of melting and lattice dynamics

Abstract

The melting and the lattice dynamics are investigated from the view-point of a quantum field theory at finite temperature (thermo field theory). Our theory starts with ion cores and valence electrons interacting with each other as the first principle. The Ward-Takahashi relations play an essential role in determining the melting temperature and constructing the lattice dynamics. Phonons in crystals are constructed by particle-hole excitations of ion cores and valence electrons. Phonon spectra, phonon propagators and the dynamical map of the density of ion cores are calculated at finite temperature. In principle, our theory covers metallic, covalent and molecular crystals. The conventional secular equation for the lattice dynamics is obtained by neglecting some quantum effects in the equation of the density-density correlation of ion cores.