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The nonrelativistic many-electron system in the forward, exchange and BCSapproximation is considered. In this approximation, which is still quartic inthe annihilation and creation operators, the model is explicitly solvable forarbitrary space dimension d. The partition function and the correlationfunctions are given by finite-dimensional integral representations.Renormalization effects as well as symmetry breaking can be seen explicitly. Itis shown that the usual mean field approach, based on approximating theHamiltonian by a quadratic expression, may be misleading if theelectron-electron interaction contains higher angular momentum terms and thespace dimension is d=3. The perturbation theory of the solvable model isdiscussed. There are cases where the logarithm of the partition function haspositive radius of convergence but the sum of all connected diagrams has radiusof convergence zero implying that the linked cluster theorem is not applicablein these cases.Comment: 47 pages, Te

The Many-Electron System in the Forward, Exchange and BCS Approximation