SU(2) coherent state path integrals based on arbitrary fiducial vectors and geometric phases

We develop the formulation of the spin(SU(2)) coherent state path integrals based on arbitrary fiducial vectors. The resultant action in the path integral expression extensively depends on the vector; It differs from the conventional one in that it has a generalized form having some additional terms. We also study, as physical applications, the geometric phases associated with the coherent state path integrals to find that new effects of the terms may appear in experiments. We see that the formalism gives a clear insight into geometric phases.