We formulate a many-body theory of a dilute quantum gas focusing specifically on the description of a scattering resonance. This situation is relevant to current experiments in atomic physics involving Feshbach resonances. In a Feshbach resonance a continuum scattering channel is degenerately coupled to an isolated bound state. The presence of such a resonance allows the interaction properties between atoms to be varied by modifying the strength of an external magnetic field. Since the interactions can be made strong this creates the possibility for entering parameter regimes in which simple perturbative theories of the gas fail.
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