We consider a cold Bose gas in the unitarity limit. The unitarity limit corresponds to the limit where the scattering length goes to infinity. In this thesis we first review basic quantummechanical scattering theory and explain the physics of Feshbach resonances. After that we discuss a many-body theory, which exactly incorporates the two-body physics of a Feshbach resonance. In a mean-field approximation we obtain a divergence of the energy per particle in the unitarity limit. Beyond mean field the spectral function is ill behaved. To get more insight into these problems, we also discuss a model of linearly coupled atoms and phonons. A generalized Bogoliubov transformation is used to obtain expressions for the quantized atomic and phonon field operators. Finally, we use these operators to calculate some correlation functions.