On the colour confinement and the minimal surface

In the analysis of the energy of the four-quark system obtained in the SU(2) lattice Monte Carlo, the f-mode in which the transition potential is expressed in the form f = fce-kAbsA-kP√bsP, where A is the area and P is the perimeter of the Wilson loop, was successful in the case of simple configurations of the four quarks. In the case of tetrahedral geometry, an estimation of the minimal surface whose contours run the positions of the four quarks is necessary. We show that the regular surface approximation whose area can be calculated analytically, is a good approximation for evaluating the minimal surface. The numerical value of the coefficient kAbs is close to 2fm-2 which is the density of the Z2 vortex in the SU(2) lattice Monte Carlo. (author)