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We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus allows first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness of the basis and derive differential forms for products with one-and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anticommuting Grassmann variables. Furthermore, because of the overcompleteness of the basis, the phase-space distribution can always be chosen positive. This has important consequences for the sign problem in fermion physics.

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Heavy fermions compounds show highly unusual properties. The most striking one is probably superconductivity. Triplet superconductivity has been suggested. Here we want to suggest that singlet superconductivity is possible. We first emphasize that heavy fermions are due to quasi localized f-electrons. Thus we show that magnetic correlations are important in this heavy Fermi liquid. Even in the non magnetic case, magnetic interactions as measured for instance by the paramagnetic Curie temperature, are greater than the Kondo temperature. This point, using a Fermi liquid theory,