  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.
