Theory of interacting bosons without anomalous propagators

A self-consistent theory of an interacting many-boson system is presented in the framework of the formalism of thermodynamic Green's functions without introducing anomalous propagators referring to the concept of a restricted average or any other symmetry-breaking assumption. Depending on the interaction, the theory comprises both phenomena of Bose-Einstein condensation and of boson pairing without a macroscopic occupation of the zero-momentum single-particle state. The results are discussed with reference to the problem of Bose-Einstein condensation of 4He II and to the phenomenon of exciton condensation and exciton pairing in highly excited semiconductors.