The solution by Einstein–Infeld–Hoffmann method the problem of colour particles motion and gauge field dynamics

The Einstein–Infeld–Hoffmann (EIH) method is used to solve the problem of self-consistent description of the dynamics of the gravitational field and Yang–Mills field in the presence of particles that generate these fields and are singular points of them. The results that follow from the Drechsler–Rosenblum equations in the lowest orders of the approximation are reproduced. It is shown that a separation of the orders of smallness compatible with these equations leads either to the disappearance of interaction between the particles or to noncompactness of the gauge group. The possible consequences of a different separation of orders allowed by the EIH-method but not compatible with the given equations are discussed.