Weak self-consistent approximation scheme in many-body systems

In this paper we show a possibility of restricting the usual self-consistency conditions in approximations to many-body systems. Instead of requiring thermodynamic consistency for even non-physical one-particle quantities, we impose it for the physically relevant quantities only. As a consequence of this less severe requirement, one does not lose any physically relevant information, but one can construct new types of approximations. As an example a parametric approximation scheme is given.