Thin and dressed Polyakov loops from spectral sums of lattice differential operators

We represent thin and dressed Polyakov loops as spectral sums of eigenvalues of differential operators on the lattice. For that purpose we calculate complete sets of eigenvalues of the staggered Dirac and the covariant Laplace operator for several temporal boundary conditions. The spectra from different boundary conditions can be combined such that they represent single (thin) Polyakov loops, or a collection of loops (dressed Polyakov loops). We analyze the role of the eigenvalues in the spectral sums below and above the critical temperature.