Noninstantaneous action-at-a-distance theory of interacting relativistic strings

A classical noninstantaneous action-at-a-distance theory of interacting relativistic strings in both Lagrangian and Hamiltonian formulations has been developed by generalizing the noninstantaneous action-at-a-distance formulation of relativistic mechanics of point particles. Parametrization invariance of the free and the interstring actions allows introduction of a common time parameter for all the strings. The Lagrangian, the resulting equations of motion, and the conserved generators are seen to be nonlocal in time. Choosing the asymptotic solutions of the equations of motion as the canonical variables, the noncovariant Hamiltonian formulation is developed in the lightlike orthonormal gauge. The conserved generators have been shown to obey the regular Lie algebra of the Poincar\'e group. The physical variables have the regular Poisson bracket properties with respect to the conserved generators.