Abelian Projection without Ambiguities

Laplacian Abelian Projection is discussed. This term refers to the use of anew (``Laplacian'') gauge fixing prescription for implementing the AbelianProjection of QCD. The gauge condition is based on the lowest-lying eigenvectorof the covariant Laplacian operator in the adjoint representation. This Laplacian gauge fixing procedure is free of the ambiguities which plaguelattice simulations which work with the popular Maximally Abelian Gauge.Furthermore, Laplacian gauge fixed configurations enjoy a natural kind ofsmoothness. These two properties are crucial for a reliable determination ofphysical quantities using the Abelian Projection. We also examine a new, Higgs-field-like observable which emerges as aby-product of the method. This quantity can be used to identify magneticmonopoles in a way independent of the traditional prescription. It is arguedthat physically relevant magnetic monopoles are accomodated well by theLaplacian method, while they are suppressed (too) strongly in Maximally AbelianGauge. Finally, first evidence of abelian dominance in the Laplacian AbelianProjection is presented.