Laplacian modes as a filter

Abstract

We compute low-lying eigenmodes of the gauge covariant Laplace operator on the lattice at finite temperature. For classical configurations we show how the lowest mode localizes the monopole constituents inside calorons and that it hops upon changing the boundary conditions. The latter effect we observe for thermalized backgrounds, too, analogously to what is known for fermion zero modes. We propose a new filter for equilibrium configurations which provides link variables as a truncated sum involving the Laplacian modes. This method not only reproduces classical structures, but also preserves the confining potential, even when only a few modes are used.Comment: talk presented by FB at the Workshop on Computational Hadron Physics, Nikosia (Cyprus), Sept. 14-17, 2005; compared to hep-lat/0509020 and hep-lat/0509087 we have added the following points: 1. the kinetic term (square of the covariant derivative) as an analyzing observable, 2. the correlation of filtered link variables to the original ones, 3. the filtered string tension from modes with shifted ordinal number; 8 pages, 8 figures, uses espcrc2.st