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We derive the low-energy effective action for three-dimensional superfluidFermi systems in the strong-coupling limit, where superfluidity originates fromBose-Einstein condensation of composite bosons. Taking into account density andpairing fluctuations on the same footing, we show that the effective actioninvolves only the fermion density $\rho_{\bf r}$ and its conjugate variable,the phase $\theta_{\bf r}$ of the pairing order parameter $\Delta_{\bf r}$. Werecover the standard action of a Bose superfluid of density $\rho_{\bf r}/2$,where the bosons have a mass $m_B=2m$ and interact {\it via} a repulsivecontact potential with amplitude $g_B=4\pi a_B/m_B$, $a_B=2a$ ($a$ the s-wavescattering length associated to the fermion-fermion interaction in vacuum). Forlattice models, the derivation of the effective action is based on the mappingof the attractive Hubbard model onto the Heisenberg model in a uniform magneticfield, and a coherent state path integral representation of the partitionfunction. The effective description of the Fermi superfluid in thestrong-coupling limit is a Bose-Hubbard model with an intersite hoppingamplitude $t_B=J/2$ and an on-site repulsive interaction $U_B=2Jz$, where$J=4t^2/U$ ($t$ and $-U$ are the intersite hopping amplitude and the on-siteattraction in the (fermionic) Hubbard model, $z$ the number of nearest-neighborsites).Comment: 9 pages (final version

Effective action for superfluid Fermi systems in the strong-coupling limit