  The Tomonaga-Luttinger model with impurity is studied by means of flow
equations for Hamiltonians. The system is formulated within collective density
fluctuations but no use of the bosonization formula is made. The truncation
scheme includes operators consisting of up to four fermion operators and is
valid for small electron-electron interactions. In this regime, the exact
expression for the anomalous dimension is recovered. Furthermore, we verify the
phase diagram of Kane and Fisher also for intermediate impurity strength. The
approach can be extended to more general one-body potentials.
