BLOCK RENORMALIZATION-GROUP APPROACH FOR CORRELATION-FUNCTIONS OF INTERACTING FERMIONS

Inspired by a decomposition of the lattice Laplacian operator into mas sive terms (coming from the use of the block renormalization group tra nsformation for bosonic systems), we establish a telescopic decomposit ion of the Dirac operator into massive terms, with a property named 'o rthogonality between scales'. Making a change of Grassmann variables a nd writing the initial fields in terms of the eigenfunctions of the op erators related to this decomposition, we propose a multiscale structu re for the generating function of interacting fermions. Due to the ort hogonality property we obtain simple formulas, establishing a trivial link between the correlation functions and the effective potential the ories. In particular, for the infrared analysis of some asymptotically free models, the two point correlation function is written as a domin ant term (decaying at large distances as the free propagator) plus a c orrection with faster decay, and the study of both terms is straightfo rward once the effective potential theory is controlled.