  We study the spin--boson model with a sub--Ohmic bath using infinitesimal
unitary transformations. Contrary to some results reported in the literature we
find a zero temperature transition from an untrapped state for small coupling
to a trapped state for strong coupling. We obtain an explicit expression for
the renormalized level spacing as a function of the bare papameters of the
system. Furthermore we show that typical dynamical equilibrium correlation
functions exhibit an algebaric decay at zero temperature.
