Classical relativistic dynamics of a system of interacting atoms: Hamiltonian form

The paper contains generalization of the nonrelativistic classical Hamiltonian dynamics of a system of interacting particles to the case of a relativistic theory. The interaction between atoms is taken into account within the concept of a covariant auxiliary field, which is equivalent to instantaneous interatomic potentials only in the nonrelativistic limit. It is established that the auxiliary field is a superposition of elementary fields, each of which satisfies the Klein-Gordon-Fock type equations. The real and complex forms of the relativistic Hamiltonian of a system of interacting particles are presented, taking into account the field degrees of freedom. The Hamiltonian contains three contributions corresponding to free particles, free fields of the Klein-Gordon- Fock type, and interactions between particles and fields. Based on the variational formulation of problems of relativistic molecular dynamics, an exact closed relativistic system of equations is obtained, describing the evolution of a system of atoms and an auxiliary field within the framework of the Hamiltonian picture. An analysis of the qualitative properties of solutions of the equations of the system's dynamics is performed.