Canonical formalism for the Born-Infeld particle

In the previous paper (hep-th/9712161) it was shown that the nonlinear Born-Infeld field equations supplemented by the "dynamical condition" (certain boundary condition for the field along the particle's trajectory) define perfectly deterministic theory, i.e. particle's trajectory is determined without any equations of motion. In the present paper we show that this theory possesses mathematically consistent Lagrangian and Hamiltonian formulations. Moreover, it turns out that the "dynamical condition" is already present in the definition of the physical phase space and, therefore, it is a basic element of the theory.