Bogoliubov theory for a many-boson system

Presently there are two distinct classes of microscopic theories which describe a system of many identical spinless bosons. One is the Bogoliubov theory, which places special emphasis on the occupation of the zero-momentum state and as such depends explicitly on the number of particles in this state, N0. The other depends on density fluctuations to describe the fluid. In this work, we derive a modified version of the Bogoliubov theory which results in a number-conserving Hamiltonian with no explicit dependence on N0. The ground- and first-excited-state energies evaluated through second order in 1N12 are equivalent to the results of a variational-perturbative procedure based on the method of correlated basis functions in the uniform limit. © 1975 The American Physical Society.