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This thesis presents theoretical work in s- and p-wave resonantly pairedFermi gases at zero temperature. In the BEC regime of the wide-resonance s-waveBCS-BEC crossover, the chemical potential, speed of sound, condensatedepletion, and ground state energy are computed. The quantities are calculatedin a low density approximation. The bosonic scattering length is computeddiagrammatically to be approximately 0.60a with a the fermionic scatteringlength, confirming a well-known result. The perturbative approach breaks downin the intermediate BCS-BEC crossover regime which is not investigated. Quantumcorrections are computed in the low density expansion, and the mass-imbalancedtwo-species Fermi gas is investigated. For identical fermions, it is discussedhow p-wave Feshbach resonances naturally fall into two classes of "weak" and"strong", depending on the short-distance physics. It is shown how boundfermionic trimers appear in the strongly-resonant superfluid. The appearance ofthe trimer under the strengthening of the resonance is investigated, and thelifetime of p-wave diatomic molecules due to collisional relaxation intotrimers is estimated.

Paired fermionic superfluids with s- and p-wave interactions