We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green’s functions. We especially focus on the description of the boson-fermion interaction. To do so we need to introduce a new relevant object, the renormalized boson-fermion T -matri...

3m (k) = dw d~S(k ,.,) for a system of Bosons of mass m at zero temperature and density n to the first approximation beyond the Bogoliubov (zeroth) approximation. The two-body interaction u is characterized by the s-wave scatteringlength and is taken to be a constant in k-space. The small dimensionless parameter g = 4irams 0, where s0 = (4iran) 1/2/m is the phonon speed in the zeroth approximat...

The dynamics of a particle which is linearly coupled to the environment of a Boson field is investigated. For velocity coupling and for local (position) coupling the reduced dynamics of the particle induces superselection rules for the momentum, if the Boson field is infrared divergent. Thereby the Hamiltonian of the total system remains bounded from below.