Loop expansion and properties of a model one-point function in an effective Hamiltonian approach to bound-state systems

A derivation is made of the expression of a model many-body one-point function, which appears in effective many-body Hamiltonians, in the framework of a loop expansion by using the replica variable technique. Specific properties of the effective Lagrangian appearing in the integral expression of the propagator are shown. The properties of the lowest-order expansion terms in the conventional saddle-point approach are analysed and other possible developments are discussed. (author)