Front form of relativistic Lagrangian dynamics in two-dimensional space-time and its connection with the Hamiltonian description

A Lagrangian relativistic theory is formulated in two-dimensional space-time in the front form of dynamics; the connection between it and predictive mechanics, the Hamiltonian description, and the theory of Fokker action integrals is established. Relations are found in a closed form without the use of formal expansions. The existence of mathematical restrictions on the values of the two-particle interaction Lagrangians is established.