  The amplitude for emitting $n$ bosons factorizes into the product of $n$
single-boson emission amplitudes, if the source is energetic and abelian. If it
is energetic but {\it non-abelian}, the amplitude is given by a sum of
factorized {\it quasi-particle} amplitudes. A quasi-particle is made up of an
arbitrary number of bosons, but couples to the source like a single one.
Factorization is related to coherence, and it allows computation of subleading
contributions not obtainable by usual means. Its importance is illustrated in
two applications: to solve the baryon problem in large-$N_c$ QCD, and to obtain
a total cross section satisfying the Froissart bound.
