A new method of expansion in the quantum many-body problem: III. The density field

In a discussion of the quantum dynamics of a non-relativistic many-particle system it is shown how a two-body interaction, quartic in the field operators, may be replaced by an interaction with an auxliary density-like field. An extension of the procedure of Edwards and Sherrington for expanding in terms of correlations about the state of maximal quantum randomness is applied to the coupled system to give the density correltions and excitations as well as the corresponding single-particle quantities. As an example, an explicit expression for the density excitations is obtained in terms of the quasi-particle energies, for the case in which quasi-particles exist as well-defined modes of single-particle excitation.