  We address the few-body problem using the adiabatic hyperspherical
representation. A general form for the hyperangular Green's function in
$d$-dimensions is derived. The resulting Lippmann-Schwinger equation is solved
for the case of three-particles with s-wave zero-range interactions. Identical
particle symmetry is incorporated in a general and intuitive way. Complete
semi-analytic expressions for the nonadiabatic channel couplings are derived.
Finally, a model to describe the atom-loss due to three-body recombination for
a three-component fermi-gas of $^{6}$Li atoms is presented.
