Complex Variational Calculus with Mean of (min, +)-analysis

ABSTRACT

One develops a new mathematical tool, the complex (min, +)-analysis which permits to define a new variational calculus analogous to the classical one (Euler-Lagrange and Hamilton Jacobi equations), but which is well-suited for functions defined from ℂⁿ to ℂ. We apply this complex variational calculus to Born-Infeld theory of electromagnetism and show why it does not exhibit nonlinear effects.

Keywords:
Variational Calculus; Lagrangian; Hamiltonian; Action; Euler-Lagrange and Hamilton-Jacobi equations; complex (min, +)-analysis; Maxwell’s equations; Born-Infeld theory