Abstract
The collective modes in a uniform fermionic atomic gas with Feshbach resonance are investigated with the path integral method in the frame of a fermion-boson model Hamiltonian. We mainly concentrated on the long-wavelength and low-frequency limits at $T=0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and got an analytical expression for the collective modes across the whole BCS-Bose-Einstein condensate (BEC) crossover. We completely recover the Anderson-Bogoliubov modes in the BCS limit and the Bogoliubov modes of the bosonic systems in the BEC limit. The numerical results show that there exists a continuous interpolation for sound velocity between BCS and BEC limits.
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