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We develop a self-consistent theory unifying the description of a quantumFermi gas in the presence of a Fano-Feshbach resonance in the whole phasediagram ranging from BCS to BEC type of superfluidity and from narrow to broadresonances, including the fluctuations beyond mean field. Our theory covers apart of the phase diagram which is not easily accessible by Quantum Monte Carlosimulations and is becoming interesting for a new class of experiments in coldatoms.

Local-field Theory of the BCS-BEC Crossover