Collective excitations and screening properties of a condensed charged Bose gas

The Bogoliubov–de Gennes (BdG) type equations are derived for the Coulomb Bose gas describing the electrodynamics of charged bosons. The gauge invariant dielectric response function and collective excitations of a charged Bose gas at T=0 are found. We find a plasmon branch which is the same as the single-particle Bogoliubov spectrum in agreement with the textbook result. The superconducting properties of the charged Bose gas are verified. A gauge-invariant formalism for calculating the response of the supracondensate particles is proposed.