Three-body relativistic flux tube model from QCD Wilson-loop approach

First we review the derivation of the relativistic flux tube model for a quark-antiquark system from the Wilson area law as we have given in a preceding paper. Then we extend the method to the three-quark case and obtain a Lagrangian corresponding to a star flux tube configuration. A Hamiltonian can be explicitly constructed as an expansion in 1m2 or in the string tension σ. In the first case it reproduces the Wilson loop three-quark semirelativistic potential; in the second one, it is very complicated in general, but it reproduces known string models for slowly rotating quarks.