Many-body green function of degenerate systems

A rigorous nonperturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H0 leading to eigenstates of H0+V for degenerate systems. These initial states are eigenstates of P0VP0, where P0 is the projection onto a degenerate eigenspace of H0. This result is used to give the proper definition of the Green function, the statistical Green function and the nonequilibrium Green function of degenerate systems. The convergence of these Green functions is established.