  The hypothesis that matter is made of some ultimate and indivisible objects,
together the restricted relativity principle, establishes a constraint on the
kind of variables we are allowed to use for the variational description of
elementary particles. We consider that the atomic hypothesis not only states
the indivisibility of elementary particles, but also that these ultimate
objects, if not annihilated, cannot be modified by any interaction so that all
allowed states of an elementary particle are only kinematical modifications of
any one of them. Terefore, an elementary particle cannot have excited states.
In this way, the kinematical group of spacetime symmetries not only defines the
symmetries of the system, but also the variables in terms of which the
mathematical description of the elementary particles can be expressed in either
the classical or the quantum mechanical description. When considering the
interaction of two Dirac particles, the atomic hypothesis restricts the
interaction Lagrangian to a kind of minimal coupling interaction.
