  Auxiliary field quantum Monte Carlo methods for Hubbard models are generally
based on a Hubbard-Stratonovitch transformation where the field couples to the
z-component of the spin. This transformation breaks SU(2) spin invariance. The
symmetry is restored only after summation over the auxiliary fields. Here, we
analyze an alternative decomposition, which conserves SU(2) spin invariance,
but requires the use of complex numbers. We show that this algorithm gets rid
of the very large fluctuations observed in imaginary time displaced correlation
functions of quantities which do not commute with the z-component of the total
spin. The algorithm prooves to be efficient for the study of spin dynamics.
