Absence of sign problem in the (saddle point approximation of the) nilpotency expansion of QCD at finite chemical potential

We have developed a method to derive the (approximate) quark contribution to the fermion free energy of QCD on a lattice, at finite temperature and chemical potential, with Kogut-Susskind fermions in the flavor basis. We show here the expression at zero temperature. This result has been obtained at the lowest order of the nilpotency expansion. At this order the well known "sign problem" does not arise and the quark contribution to the action can be used as a statistical weight in the Monte Carlo simulations.