Canonical formalism for the Born-Infeld particle

TL;DR

This paper develops a consistent Lagrangian and Hamiltonian formalism for the Born-Infeld particle theory, showing that the boundary condition is fundamental to the physical phase space and determinism of the model.

Contribution

It introduces a mathematically consistent canonical formalism for the Born-Infeld particle, emphasizing the fundamental role of the dynamical boundary condition.

Findings

Established Lagrangian and Hamiltonian formulations for the theory

Demonstrated the boundary condition's role in defining the phase space

Confirmed the theory's deterministic nature without additional equations

Abstract

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.