  The Cl(3,0) Clifford algebra is represented with the commutative ring of
hyperbolic numbers H. The canonical form of the Poincare mass operator defined
in this vector space corresponds to a sixteen-dimensional structure. This
conflicts with the natural perception of a four-dimensional space-time. The
assumption that the generalized mass operator is an hermitian observable forms
the basis of a mathematical model that decomposes the full sixteen-dimensional
symmetry of the hyperbolic Hilbert space. The result is a direct product of the
Lorentz group, the four-dimensional space-time, and the hyperbolic unitary
group SU(4,H), which is considered as the internal symmetry of the relativistic
quantum state. The internal symmetry is equivalent to the original form of the
Pati-Salam model.
