In an atomic gas near a Feshbach resonance, the energy of two colliding atoms is close to the energy of a bound state, i.e., a molecular state, in a closed channel that is coupled to the incoming open channel. Due to the different spin arrangements of the atoms in the open channel and the atoms in the molecular state, the energy difference between the bound state and the two-atom continuum threshold is experimentally accessible by means of the Zeeman interaction of the atomic spins with a magnetic field. As a result, it is in principle possible to vary the scattering length to any value by tuning the magnetic field. This level of experimental control has opened the road for many beautiful experiments, which recently led to the demonstration of coherence between atoms and molecules. This is achieved by observing coherent oscillations between atoms and molecules, analogous to coherent Rabi oscillations that occur in ordinary two-level systems. We review the many-body theory that describes coherence between atoms and molecules in terms of an effective quantum field theory for Feshbach-resonant interactions. The most important feature of this effective quantum field theory is that it incorporates the two-atom physics of the Feshbach resonance exactly, which turns out to be necessary to fully explain experiments with Bose-Einstein condensed atomic gases.

100 pages, 34 figures, review paper submitted to Phys. Rep