  We present a formulation of the Constrained Path Monte Carlo (CPMC) method
for fermions that uses trial wave-functions that include many-body effects.
This new formulation allows us to implement a whole family of generalized
mean-field states as constraints. As an example, we calculated superconducting
pairing correlation functions for the two-dimensional repulsive Hubbard model
using a BCS trial state as the constraint. We compared the results with the
case where a free-electron trial wave-function is used. We found that the
correlation functions are independent of which state is used as the constraint,
which reaffirms the results previously found by Zhang et. al regarding the
suppression of long range pairing correlations as the system size increases.
