The inverse problem within free electrodynamics and the coisotropic embedding theorem (Q6564980)

This work focuses on the inverse problem of the calculus of variations (first considered by Helmholz in 1887). The author reviewed two existing formulations of the problem; one of them is a Lagrangian formulation coming from theoretical physics literature (inverse problem of Poisson dynamics) which is also of interest in the field of information theory. A review of main results for the inverse problem is given. An alternative approach to the problem for the case of free Electrodynamics in vacuum is the main focus of the current work. In particular, the the main goal is to show the existence of a solution in the chosen setting by using a generalization of a result in [\textit{L. A. Ibort} and \textit{J. Marín Solano}, Inverse Probl. 7, No. 5, 713--725 (1991; Zbl 0756.34019)]. The equations of motion of free Electrodynamics in vacuum are formulated in terms of a family of vector fields over a pre-symplectic manifold and an existence result for the inverse problem using the coisotropic embedding theorem is provided.