Bosonization and Functional Renormalization Group Approach in the Framework of QED_2

Known results on two-dimensional quantum electrodynamics (QED_2) have been used to study the dependence of functional renormalization group equations on renormalization schemes and approximations applied for its bosonized version. It is demonstrated that the singularity of flow equations can be avoided in the optimized and power-law schemes for the bosonized model and the drawback of renormalization on bosonization is shown: it is indicated that renormalization of QED_2 possibly requires interaction terms corresponding to higher frequency modes of its bosonized version.