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(Stony Brook University)
Auletta A1 (LNF)
Via Enrico Fermi, 40
00044 Frascati (Roma)
Because of the phase of the fermion determinant lattice QCD at nonzero
chemical potential cannot be simulated by standard stochastic algorithms.
However, if the sign problem is not severe, various independent methods
give consistent results. We will investigate the severity of the
sign problem by means of chiral perturbation theory. The distribution
of the average phase factor, the chiral condensate and the baryon number will
be derived and the overlap problem will be discussed.
We compare various observables evaluated in QCD and in phase quenched QCD
and give quantitative estimates for the contribution due to the phase of the
fermion determinant. We will ask the question if there is a preferred class
of observables with weak correlations with the phase factor which can be
evaluated despite a severe sign problem. The relation between the Dirac
spectrum and the sign problem will be discussed. We will illustrate these
questions by explicit calculations in one dimensional lattice QCD and random
matrix theory. Finally, implications for other nonhermitean Dirac
operators suchas the Wilson Dirac operator at nonzero lattice spacing will