  The explanation of the photoelectric effect by Einstein and Maxwell's field
theory of electromagnetism have motivated De Broglie to make the hypothesis
that matter exhibits both waves and particles like-properties. These
representations of matter are enlightened by string theory which represents
particles with stringlike entities. Mathematically, string theory can be
formulated with a gauge theory on loop spaces which is equivalent to the
differential geometry of gerbes. In this paper, we show that the descent theory
of Giraud and Grothendieck can enable to describe the wave-like properties of
the matter with the quantization of a theory of particles. The keypoint is to
use the fact that the state space is defined by a projective bundle over the
parametrizing manifold which induces a gerbe which represents the geometry
obstruction to lift this bundle to a vector bundle. This is equivalent to
saying that a phase is determined up to a complex number of module $1$. When
this uncertainty occurs, we cannot locate precisely the position of a particle,
and the smallest dimensional quantity that can be described is a $1$
dimensional manifold; this leads to the concept of wave properties of the
matter and string theory.
