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 C^n 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