Theory of a Charged Bose Gas. I

This is the first of two papers in which the high-density charged Bose gas at zero temperature is treated by two independent and self-contained methods. In this paper, we are concerned with the excitation spectrum of the system. An analysis of the formal and physical aspects of the theory is followed by a simple numerical calculation. We apply the usual field-theoretic formulation for a Bose system. The Green's functions and other response functions, or propagators, are analyzed, emphasizing the role of the dielectric constant. The general features of the excitation spectrum are described. To apply and to further illustrate the formalism, the low-lying levels are numerically determined to the order of ${r_s}^{\frac{3}{4}}$ in units of ${\omega }_{\mathrm{pl}}$ (the next order beyond the Bogoliubov approximation). $r_s$ is the ratio of the average interparticle distance to the Bohr radius and ${\omega }_{\mathrm{pl}}$ is the plasma frequency.