The many-body problem within the Lee model

The structure of a field theoretical many-body problem is studied within the (non-static) Lee model. The explicit solvability of the renormalization problem allows the investigation of renormalization corrections in many-particle systems. Herefore, the renormalized equations are worked out for the N-V scattering and for the binding-energy problem of “N-V matter” — these cases taken in analogy to nucleon-nucleon scattering and nuclear matter. The N-V matter equations are obtained from a cluster expansion suitably defined for the field theoretical case. The ansatz for the correlated wave functions is chosen in such a way as to generate a two-hole-line expansion of the binding energy. The renormalized form of this field theoretical extension of Brueckner theory is discussed in detail revealing the medium effects on renormalization.