Treatment of many levels in QCD

Abstract A method is proposed how to deal non-pertubatively with more than one level (of boson and fermion states) in a finite volume. It consists of two steps. The first one is given by a boson mapping, exploiting the perturbative result that certain pairs (e.g. of spin-colour zero) are strongly lowered in energy, thus indicating a pair structure. In the second step collective boson-pairs of definite colour and spin are introduced which are thought to dominate in the low energy region. They are a coherent sum of all possible pairs with the same colour and spin. The composition is determined via a standard variational procedure. The end product is an effective Hamiltonian which depends only on the collective pairs and thus is of one or few mode type. The method is tested at a toy model.