THE MANY-ELECTRON SYSTEM IN THE FORWARD, EXCHANGE AND BCS APPROXIMATION

The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, the model is e xplicitly solvable for arbitrary space dimension d. The partition func tion and the correlation functions are given by finite-dimensional int egral representations. Renormalization effects as well as symmetry bre aking can be seen explicitly. It is shown that the usual mean field ap proach, based on approximating the Hamiltonian by a quadratic expressi on, may be misleading if the electron-electron interaction contains hi gher angular momentum terms and the space dimension is d = 3. The pert urbation theory of the solvable model is discussed. There are cases wh ere the logarithm of the partition function has positive radius of con vergence but the sum of all connected diagrams has radius of convergen ce zero implying that the linked cluster theorem is not applicable in these cases.