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A new partial gauge fixing condition for the abelian projection is introduced. It is based on the lowest-lying eigenvector of a covariant Laplacian operator. This gauge is smooth and free of lattice Gribov copies. These properties are important for an unambiguous computation of the abelian projected gauge field configuration.

The magnetic monopole in euclidean pure SU(2) gauge theory is investigated using a background eld method on the lattice. With Monte Carlo methods we study the mass of the monopole in the full quantum theory. The monopole background under the quantum uctuations is induced by imposing xed monopole boundary conditions on the walls of a nite lattice volume. By varying the gauge coupling it is possible to study monopoles with scales from the hadronic scale up to high energies. The results for the monopole mass are consistent with a conjecture we made previously in a realization of the dual superconductor hypothesis of con nement.