  We present a detailed derivation of the semiclassical propagator in the SU(n)
coherent state representation. In order to provide support for immediate
physical applications, we restrict this work to the fully symmetric irreducible
representations, which are suitable for the treatment of bosonic dynamics in n
modes, considering systems with conservation of total particle number. The
derivation described here can be easily extended to other classes of coherent
states, thus representing an alternative approach to previously published
methods.
