Abstract
The applicability of the multiplicative renormalization approach to onedimensional Fermi systems is further investigated. By extending the calculation to arbitrary energy variables it is proved that at least up to second order the reduced vertices and the Green's function do obey the renormalization group equations with renormalization factors independent of the energy variables. The Lie equations for the two-variable vertex are discussed. The vertices have been determined for special choices of the energy variables and agreement with the parquet diagram summation is obtained.
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