The de Broglie Wave as a Localized Excitation of the Action Function

TL;DR

This paper revisits the Hamilton-Jacobi equation in relativistic quantum mechanics, proposing that de Broglie waves are localized excitations of the classical action function, with solutions resembling breathers that exhibit particle and wave characteristics.

Contribution

It introduces a formalism where de Broglie waves are modeled as localized breathers of the action function, offering a new perspective on quantum wave-particle duality.

Findings

Solutions in the form of breathers are possible within the Hamilton-Jacobi framework.

De Broglie waves are interpreted as localized excitations of the action function.

The formalism provides insights into quantization via breathing action functions.

Abstract

The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (nondispersive oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior adaptable to the properties of the de Broglie clock. Within this formalism the de Broglie wave acquires the meaning of a localized excitation of the classical action function. The problem of quantization in terms of the breathing action function is discussed.