Abstract

Given the eikonal equation σ i=1 3 (∂ψ/∂x i ) 2 =n′ 2, we investigate the geometric structure that underlies the law of propagation of the wavefronts ψ(x 1,x 2,x 3) —ct=0. It turns out that Huygens' principle for the propagation of wavefronts is given in terms of a contact structure. Wavefronts are carried into wavefronts by contact transformations. As regards the wave-particle duality principle that arises in quantum mechanics, there is a natural geometric structure, a symplectic manifold (M 2n , Ω), which “unifies” Fermat's principle and the eikonal equation (Huygens' principle)