  We present a comprehensive analysis of quantum fluctuation effects in the
superfluid ground state of an attractively interacting Fermi system, employing
the attractive Hubbard model as a prototype. The superfluid order parameter,
and fluctuations thereof, are implemented by a bosonic Hubbard-Stratonovich
field, which splits into two components corresponding to longitudinal and
transverse (Goldstone) fluctuations. Physical properties of the system are
computed from a set of approximate flow equations obtained by truncating the
exact functional renormalization group flow of the coupled fermion-boson
action. The equations capture the influence of fluctuations on non-universal
quantities such as the fermionic gap, as well as the universal infrared
asymptotics present in every fermionic superfluid. We solve the flow equations
numerically in two dimensions and compute the asymptotic behavior analytically
in two and three dimensions. The fermionic gap \Delta is reduced significantly
compared to the mean-field gap, and the bosonic order parameter \alpha, which
is equivalent to \Delta in mean-field theory, is suppressed to values below
\Delta by fluctuations. The fermion-boson vertex is only slightly renormalized.
In the infrared regime, transverse order parameter fluctuations associated with
the Goldstone mode lead to a strong renormalization of longitudinal
fluctuations: the longitudinal mass and the bosonic self-interaction vanish
linearly as a function of the scale in two dimensions, and logarithmically in
three dimensions, in agreement with the exact behavior of an interacting Bose
gas.
