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

Static quark-antiquark potential and Dirac eigenvector correlators

We represent the Polyakov loop correlator as a spectral sum of correlators of eigenvectors of the lattice Dirac operator. This spectral representation is studied numerically using quenched SU(3) configurations below and above the deconfinement temperature. We analyze whether the individual Dirac eigenvector correlators differ in the confined and deconfined phases. The decay properties of the no...

Dressed Polyakov loops and center symmetry from Dirac spectra

We construct a novel observable for finite temperature QCD that relates confinement and chi-ral symmetry. It uses phases as boundary conditions for the fermions. We discuss numerical and analytical aspects of this observable, like its spectral behavior below and above the critical temperature, as well as the connection to chiral condensate and center symmetry.

The Sums and Products of Commuting AC-Operators

Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.  

Dual condensate, dressed Polyakov loops and center symmetry from Dirac spectra

We construct a novel observable for finite temperature QCD that relates confinement and chi-ral symmetry. It uses phases as boundary conditions for the fermions. We discuss numerical and analytical aspects of this observable, like its spectral behavior below and above the critical temperature, as well as the connection to chiral condensate, center symmetry and the canonical ensemble.

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators