Phase of the Fermion Determinant for QCD at Finite Chemical Potential

In this lecture we discuss various properties of the phase factor of the fermion determinant for QCD at nonzero chemical potential. Its effect on physical observables is elucidated by comparing the phase diagram of QCD and phase quenched QCD and by illustrating the failure of the Banks-Casher formula with the example of one-dimensional QCD. The average phase factor and the distribution of the phase are calculated to one-loop order in chiral perturbation theory. In quantitative agreement with lattice QCD results, we find that the distribution is Gaussian with a width $\sim \mu T \sqrt V$ (for $m_\pi \ll T \ll \Lambda_{\rm QCD}$). Finally, we introduce, so-called teflon plated observables which can be calculated accurately by Monte Carlo even though the sign problem is severe.