Two-Loop Fermionic Integrals in Perturbation Theory on a Lattice

Abstract

A comprehensive number of one-loop integrals in a theory with Wilson fermions at $r=1$ is computed using the Burgio-Caracciolo-Pelissetto algorithm. With the use of these results, the fermionic propagator in the coordinate representation is evaluated, thus making it possible to extend the Luscher-Weisz procedure for two-loop integrals to the fermionic case. Computations are performed with FORM and REDUCE packages.

Comments: 7 pages; a contribution to the Workshop ACAT-2010, Jaipur, India, Feb.22-27, 2010