  We present in detail a simple, exact solution of the anisotropic 2-channel
Kondo (2CK) model at its Toulouse point. We reduce the model to a quadratic
resonant-level model by generalizing the bosonization-refermionization approach
of Emery and Kivelson to finite system size, but improve their method in two
ways: firstly, we construct all boson fields and Klein factors explicitly in
terms of the model's original fermion operators $c_{k \sigma j}$, and secondly
we clarify explicitly how the Klein factors needed when refermionizing act on
the original Fock space. This enables us to explicitly follow the adiabatic
evolution of the 2CK model's free-fermion states to its exact eigenstates,
found by simply diagonalizing the resonant-level model for arbitrary magnetic
fields and spin-flip coupling strengths. In this way we obtain an {\em
analytic} description of the cross-over from the free to the non-Fermi-liquid
fixed point. At the latter, it is remarkably simple to recover the conformal
field theory results for the finite-size spectrum (implying a direct proof of
Affleck and Ludwig's fusion hypothesis). By analyzing the finite-size spectrum,
we directly obtain the operator content of the 2CK fixed point and the
dimension of various relevant and irrelevant perturbations. Our method can
easily be generalized to include various symmetry-breaking perturbations.
Furthermore it establishes instructive connections between different
renormalization group schemes such as poor man's scaling, Anderson-Yuval type
scaling, the numerical renormalization group and finite-size scaling.
