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 $H_0$ leading to eigenstates of $H_0+V$ for degenerate systems. These initial states are eigenstates of $P_{0}V{P}_0$, where $P_0$ is the projection onto a degenerate eigenspace of $H_0$. 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.

Figure 1

Example of allowed eigenvalue pattern.