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A set of universal relations between various properties of any few-body ormany-body system consisting of fermions with two spin states and a large butfinite scattering length have been derived by Shina Tan. We derivegeneralizations of the Tan relations for a two-channel model for fermions neara Feshbach resonance that includes a molecular state whose detuning energycontrols the scattering length. We use quantum field theory methods, includingrenormalization and the operator product expansion, to derive these relations.They reduce to the Tan relations as the scattering length is made increasinglylarge.

Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance