  A formalism for studying the dynamics of quantum systems embedded in
classical spin baths is introduced. The theory is based on generalized
antisymmetric brackets and predicts the presence of open-path off-diagonal
geometric phases in the evolution of the density matrix. The weak coupling
limit of the equation can be integrated by standard algorithms and provides a
non-Markovian approach to the computer simulation of quantum systems in
classical spin environments. It is expected that the theory and numerical
schemes presented here have a wide applicability.
