Bogolyubov--Zubarev description of a weakly interacting Bose gas

Bogoliubov-Zubarev's exact transformation, specific to a weakly interacting Bose gas having a condensate, yields a Hamiltonian describing a gas of interacting excitations. The non-Hermiticity of the Hamiltonian arises from the nonorthogonality of the physical states; it has some significant consequences. The excitation spectrum is gapless in every approximation; the lowest-order correction is evaluated numerically and shown to be small. It is concluded that the approach presents a prospective method for a quantitative description of the weakly interacting Bose gas.