Forms of relativistic dynamics in a classical Lagrangian description of a system of particles

The concept of a form of relativistic dynamics in the classical theory of direct interactions of particles is associated with the foliation of Minkowski space, which determines in it a simultaneity relation and makes it possible to introduce a unique evolution parameter for any set of worldlines. A three-dimensional description of a relativistic system of particles in an arbitrary form of dynamics is developed, and conditions of Poincaré invariance of the Lagrangian formalism are found. A group-theoretical classification of the possible forms of relativistic dynamics is obtained and some concrete forms of dynamics, including the instant, front, and point forms introduced by Dirac, are discussed.