On the theory of de Broglie waves in space-time

Abstract

This paper deals with the connection between generally co-variant Hamiltonian formalism and wave processes in space-time. It is indicated that the Hamilton-Jacobi equation (H.-J. e.) is representing the characteristic condition for a nonlinear second-order differential equation of the hyperbolic type that describes a wave process in spacetime. The wave 4-velocity of wave process is the same as the particle 4-velocity (ray velocity) and is equal to one. The equality of wave velocity and the ray velocity enable us to put the point and wave model of particle into mutual correlation.