  Born proposed a unification of special relativity and quantum mechanics that
placed position, time, energy and momentum on equal footing through a
reciprocity principle and extended the usual position-time and energy-momentum
line elements to this space by combining them through a new fundamental
constant. Requiring also invariance of the symplectic metric yields U(1,3) as
the invariance group, the inhomogeneous counterpart of which is the canonically
relativistic group CR(1,3) = U(1,3) *s H(1,3) where H(1,3) is the Heisenberg
Group in 4 dimensions and "*s" is the semidirect product. This is the
counterpart in this theory of the Poincare group and reduces in the appropriate
limit to the expected special relativity and classical Hamiltonian mechanics
transformation equations. This group has the Poincare group as a subgroup and
is intrinsically quantum with the Position, Time, Energy and Momentum operators
satisfying the Heisenberg algebra. The representations of the algebra are
studied and Casimir invariants are computed. Like the Poincare group, it has a
little group for a ("massive") rest frame and a null frame. The former is U(3)
which clearly contains SU(3) and the latter is Os(2) which contains SU(2)*U(1).
