  Sterile neutrinos are known to be hypothetical neutrinos which do not
interact via the fundamental interactions described within the Standard Model
of Particles Physics i.e. electroweak and strong interactions. They are
expected to be important for the understanding of the physics beyond the
current Standard Model. In the present work, it is shown that the existence of
these particles can be suggested from covariance principle using a covariance
group formed by Linear Canonical Transformations (LCTs) associated to a
pentadimensional pseudo-Euclidian space. It is established that a spin
representation of the LCT group gives a particle classification, applicable to
the three families of leptons and quarks, which leads to the prediction of the
existence of three sterile neutrinos and their antiparticles
