  We investigate the fluctuation effect of the di-fermion field in the
crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein
condensate (BEC) in a relativistic superfluid. We work within the boson-fermion
model obeying a global U(1) symmetry. To go beyond the mean field approximation
we use Cornwall-Jackiw-Tomboulis (CJT) formalism to include higher order
contributions. The quantum fluctuations of the pairing condensate is provided
by bosons in non-zero modes, whose interaction with fermions gives the
two-particle-irreducible (2PI) effective potential. It changes the crossover
property in the BEC regime. With the fluctuations the superfluid phase
transition becomes the first order in grand canonical ensemble. We calculate
the condensate, the critical temperature $T_{c}$ and particle abundances as
functions of crossover parameter the boson mass.
