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A first attempt to understand hadron dynamics at low energies in terms of the fundamental quark and gluon degrees of freedom incorporates the effects of the gluonic field into a potential depending only on the spatial positions of the quarks, which are considered in the infinite mass limit. A suitable framework for calculating such potentials between static quarks, i.e. a generalization of the Wilson loop will be discussed.Making a connection with recent Monte Carlo lattice simulations for the lowest two energies of a system of two quarks and two antiquarks, the static qqqq-potential will be calculated in perturbation theory to fourth order. The result will be shown to be exactly equal to the prediction of a straightforward two-body approach, which in Monte Carlo lattice simulations has been found to be a reasonable approximation for very small interquark distances. *

Energies of four-quark systems calculated by the static quenched SU(2) lattice Monte Carlo method are analyzed in 2 × 2 bases for square, rectangle, tilted rectangle, linear and quadrilateral geometry configurations and in 3 × 3 bases for a non-planar geometry configuration. For small interquark distances, a lattice effect is taken into account by considering perimeter dependent terms which are characterized by the cubic symmetry. It is then found that a parameter f -that can be identified as a gluon field overlap factor -is rather well described by the form, where A and P are the area and perimeter mainly defined by the positions of the four quarks, b s is the string constant in the 2-quark potentials and E, F are constants. 0 1. Fit eigen-energies of all the (r, d) sets directly.

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