ACTION-AT-A-DISTANCE AND RADIATION REACTION OF POINT-LIKE PARTICLES IN DE SITTER SPACE

The two-particle system with the time-asymmetric retarded-advanced electromagnetic interaction known as the Staruszkiewicz-Rudd-Hill model is considered in the de Sitter space-time. The manifestly covariant descriptions of the model within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the model is de Sitter-invariant and integrable. An explicit solution of the equations of motion is derived. We use the covariant electromagnetic Green function in the de Sitter space in order to derive the equation of motion of a point charge in an external electromagnetic field, where the radiation reaction is taken into account.