A quantum field theory of excitations in a bose-condensed liquid

The dielectric formulation for the excitations in a bose-condensed liquid is developed from the viewpoint of the spontaneous breakdown of the phase symmetry. The excitations are hybridized between the sound and the atomic excitations in the normal state through the condensate. The sound and the energy band of atoms are constructed by a two-band model composed of the intraband and interband density fluctuations taking into account the random distribution of atoms. The sound is calculated in the long wavelength regime and extended to the maxon regime. The lowest energy band of the atoms behaves as the zeroth Bessel function with the negative sign due to the radial distribution function; the maximum and the minimum values of the dispersion curve of atoms locate in the vicinity of the corresponding positions of the maxon and the roton.