ABSTRACT
The wave mechanics, with its quantum amendment, brings an important point to fore: a specific intervention of the geometry, in fact, of the differential geometry. The main result of Sir Michael Berry’s work on the geometry required by the existence of arbitrary phase factors makes its mark, showing that the nonstationary Schrödinger equation means much more than usually thought, when taken from the perspective of fundamental knowledge. There is a ‘Berry moment’ of the human knowledge, which carries, among others, the precise meaning of liberating the knowledge from the lock-up of adiabaticity, and this is reflected in the general attributes of this landmark of physics. The electromagnetic fields are, in general, Yang-Mills fields to be described in a geometry of the manifold of positions of Kepler orbits of classical material points. That geometry is a geometry of sl(2,R) Riemannian space. A Hertz material particle can be characterized exactly in the manner in which Schrödinger describes the color continuum.
