Elementary excitations in superfluid liquid helium based on the Bogoliubov-Zubarev formalism

The Bogoliubov-Zubarev (BZ) formulation of the superfluid Bose liquid in terms of density as a collective variable leads to a non-Hermitian Hamiltonian (HBZ) for describing the elementary excitations. An appropriate mathematical framework for dealing with non-Hermitian operators is here employed for the first time to develop schemes for studying the elementary excitations of the Bose liquid. The energies of the ground and the first excited states associated with HBZ in "perturbation" theory are derived. A consistent scattering theory appropriate to HBZ is also given from which the two-roton scattering amplitude in the leading order of "perturbation" theory is explicitly deduced. A finite-temperature Green's-function theory is also presented. These results are shown to be equivalent to those based on the Sunakawa Hamiltonian. Results for the energy spectrum are also shown to be equivalent with those evaluated by means of a variation-perturbation procedure based on the method of correlated basis functions in the uniform limit. © 1974 The American Physical Society.