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We study a multigrid method for nonabelian lattice gauge theory, the timeslice blocking, in two and four dimensions. For SU(2) gauge fields in twodimensions, critical slowing down is almost completely eliminated by thismethod. This result is in accordance with theoretical arguments based on theanalysis of the scale dependence of acceptance rates for nonlocal Metropolisupdates. The generalization of the time slice blocking to SU(2) in fourdimensions is investigated analytically and by numerical simulations. Comparedto two dimensions, the local disorder in the four dimensional gauge field leadsto kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint  MS-TPI-94-

Multigrid Monte Carlo algorithms for SU(2) lattice gauge theory: Two versus four dimensions