The fermion propagator matrix in lattice QCD

Abstract

The fermion propagator matrix is introduced and analyzed in lattice QCD. It can be related directly to the inverse of the fermion matrix and is similar in some ways to the transfer matrix. It is shown how the Lanczos algorithm can be used to diagonalise it and this is illustrated by calculating the eigenvalues on 4 4 QCD configurations and relating the results to finite-density calculations of the chiral condensate and quark currents. This sets the groundwork for calculations on larger lattices which should, in principle, give the hadron spectrum in a way which has some advantages over usual methods.