The role of zero modes for the infrared behavior of QCD

We analyse the mechanism in which zero modes lead to an elimination of fermionic color non–singlet states in 1+1 dimensions. Using a hamiltonian lattice formulation we clarify the physical meaning of the zero modes but we do not find support for speculations on the crucial importance of lower dimensional fields (zero modes in 1+1 dimension) for the infrared behavior of QCD in 2+1 or higher dimensions.