Block Renormalization Group Approach for Correlation Functions of Interacting Fermions

Inspired on a decomposition of the lattice Laplacian operator into massive terms (coming from the use of the block renormalization group transformation for bosonic systems), we establish a telescopic decomposition of the Dirac operator into massive terms, with a property named \orthogonality between scales". Making a change of Grassmann variables and writing the initial elds in terms of the eigenfunctions of the operators related to this decomposition, we propose a multiscale structure for the generating function of interacting fermions. Due to the orthogonal property we obtain simple formulas, establishing a trivial link between the correlation function and the eeective potential theories. In particular, the correlation function formulas for some asymptotically free models separate the infrared dominant decay, and their analysis is straightforward once the eeective potential theory is controlled.