Next, we connect several previously developed methods with the current approach in the language of the SU (N ) mapping formalism. As we have discussed, the underlying EOMs for the SU (N ) approach (within the linearization approximation) are identical to Ehrenfest dynamics and the MMST-based approach under a specific choice of r s . Nuclear initial conditions for all of these methods are also obtained from the Wigner transform of the initial nuclear density operator.