  We review the study of the superfluid phase transition in a system of
fermions whose interaction can be tuned continuously along the crossover from
Bardeen-Cooper-Schrieffer (BCS) superconducting phase to a Bose-Einstein
condensate (BEC), also in the presence of a spin-orbit coupling. Below a
critical temperature the system is characterized by an order parameter.
Generally a mean field approximation cannot reproduce the correct behavior of
the critical temperature $T_c$ over the whole crossover. We analyze the crucial
role of quantum fluctuations beyond the mean-field approach useful to find
$T_c$ along the crossover in the presence of a spin-orbit coupling, within a
path integral approach. A formal and detailed derivation for the set of
equations useful to derive $T_c$ is performed in the presence of Rashba,
Dresselhaus and Zeeman couplings. In particular in the case of only Rashba
coupling, for which the spin-orbit effects are more relevant, the two-body
bound state exists for any value of the interaction, namely in the full
crossover. As a result the effective masses of the emerging bosonic excitations
are finite also in the BCS regime.
