  Wave-particle duality, together with the concept of elementary particles, was
introduced by de Broglie in terms of intrinsically "periodic phenomena".
However, after nearly 90 years, the physical origin of such undulatory
mechanics remains unrevealed. We propose a natural realization of the de
Broglie "periodic phenomenon" in terms of harmonic vibrational modes associated
to space-time periodicities. In this way we find that, similarly to a vibrating
string or a particle in a box, the intrinsic recurrence imposed as a constraint
to elementary particles represents a fully consistent quantization condition.
The resulting classical cyclic dynamics formally match ordinary relativistic
Quantum Mechanics in both the canonical and Feynman formulations. Interactions
are introduced in a geometrodynamical way, similarly to general relativity, by
simply considering that variations of kinematical state can be equivalently
described in terms of modulations of space-time recurrences, as known from
undulatory mechanics. We present this novel quantization prescription from a
historical prospective.
