  It is commonly claimed in the recent literature that certain solutions to
wave equations of positive energy of Dirac-type with internal variables are
characterized by a non-thermal spectrum. As part of that statement, it was said
that the transformations and symmetries involved in equations of such type
correspond to a particular representation of the Lorentz group. In this paper
we give the general solution to this problem emphasizing the interplay between
the group structure, the corresponding algebra and the physical spectrum. This
analysis is completed with a strong discussion and proving that: i) the
physical states are represented by coherent states; ii) the solutions in
previous references [1] are not general, ii) the symmetries of the considered
physical system in [1] (equations and geometry) do not correspond to the
Lorentz group but to the fourth covering: the Metaplectic group Mp(n).
