Massless Yang-Mills field and many-body potentials

Many-body potentials between scalar particles generated by the exchange of massless Yang-Mills gauge bosons are calculated in the classical and static limits. In the calculation of the static four-body potential, we have encountered a curious term which is proportional to h-2. It does not contribute to the diagonal elements of the potential, but it contributes to the off-diagonal elements of the potential. This term can also be found in the Fokker-type Lagrangian derived by classical methods. In order to remove this curious term, we must restrict the meaning of ''classical limit.'' In this restricted sense of the classical limit, only the two-body potential in the lowest order of approximation survives in the static limit