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The Tomonaga-Luttinger model with impurity is studied by means of flowequations for Hamiltonians. The system is formulated within collective densityfluctuations but no use of the bosonization formula is made. The truncationscheme includes operators consisting of up to four fermion operators and isvalid for small electron-electron interactions. In this regime, the exactexpression for the anomalous dimension is recovered. Furthermore, we verify thephase diagram of Kane and Fisher also for intermediate impurity strength. Theapproach can be extended to more general one-body potentials.Comment: 10 pages, 1 figur

Tomonaga-Luttinger model with an impurity for a weak two-body interaction