A strongly interacting Fermi gas, such as that of cold atoms operative near a Feshbach resonance, is difficult to study by perturbative many-body theory to go beyond mean field approximation. Here I develop an effective field theory for the resonant superfluid based on broken symmetry. The theory retains both fermionic quasiparticles and superfluid phonons, the interaction between them being derived non-perturbatively. The theory converges and can be improved order by order, in a manner governed by a low energy expansion rather than by coupling constant. I apply the effective theory to calculate the specific heat and propose a mechanism of understanding the empirical power law of energy versus temperature recently measured in a heat capacity experiment.

4+ pages, 1 figure; Added references, corrected and clarified minor statements (v.2)