Wilson-Kadanoff Renormalization Group in Higher Orders: One-Dimensional g-ology Model as an Example

We apply the standard Wilson-Kadanoff (WK) momentum-space Renormalization Group (RG) scheme for the g-ology model of one-dimensional fermions. By explicitly carrying out calculations at the two-loop level, we show how the RG flow equations can be derived from the summation of the cascades of contractions generated by the effective action's mode elimination at each infinitesimal step of the WK procedure. The rules for selecting these series of cascades appear naturally as a consequence of the WK scheme ``on-shell'' kinematic constraints and conservation laws. The relation between the present RG approach and the field-theoretic schemes used in earlier related studies is analysed. Generalizations for other models and/or higher dimensions are formulated.