  The diffculties of relativistic particle theories formulated my means of
canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led
theoretical physicists to turn on quantum field theory to model elementary
particle physics. The aim of the present work is to pursue a method alternative
to canonical quantization that avoids these dfficulties. In order to guarantee
this result, the present approach is constrained to be developed deductively
from physical principles. The physical principles assumed for a free particle
consist of the symmetry properties of the particle with respect to the
Poincar\'e group and of the transformation properties of the position
observable, expressed by means of a suitably conceived notion of quantum
transformation. In so doing, the effectiveness of group theoretical methods is
exploited. Our work has pointed out the necessity of new classes of irreducible
representations of the Poincar\'e group the theory can be based on. For spin 0
particle, four inequivalent theories are completely determined, that differ
from Klein-Gordon theory for the physical interpretation but also for the
mathematical structures. In particular, two of these theories requires
irreducible representations in the new classes. The present lack of the
explicit transformation properties of position with respect to boosts forbids
the complete determination of non zero spin particle theories. A particular
form of these transformation properties was in past adopted by Jordan and
Mukunda. We check its consistency within the present approach; it is found that
for spin 1/2 particles there is only one consistent theory; it is unitarily
related to Dirac theory, but, once again, it requires the new classes of
irreducible representations.
