Nucleon properties in a few mode bag — an effective approximation to QCD

The Hamiltonian of Quantum Chromodynamics is approximated by restricting the spatial dependencies of the quark-antiquark and gluon fields to a small number of modes (few-mode approximation). As a working hypothesis, we assume that the ground states of the dynamical sectors of the theory are automatically gauge invariant so that Gauss's law need not be strictly satisfied by a trial state. We derive and apply a method for explicit calculation of expectation values for wavefunctions in colour space depending on the twoSU (3) invariants acting as dynamical variables. An interacting ground state is constructed by a dynamical dressing transformation of the bare fermionic vacuum which may be regarded as a few-mode approximation to a quark-gluon (or mesonic) condensate. Based on this vacuum a nucleon state is formulated quite similar to the solition bag construction. Some of its effective properties are calculated by a variational calculation and comparison is made with experimental data as well as with other theoretical models of bag-type.