The unitary irreducible representations of the covering group of the Poincaré group P define the framework for much of particle physics on the physical Minkowski space M = P êê ê ê L êêê , where L is the Lorentz group. While extraordinarily successful, it does not provide a large enough group of symmetries to encompass observed particles with a SU(3) classification. Born proposed the reciprocity principle that states physics must be invariant under the reciprocity transform that is heuristically8t, e, q i , p i < Ø 8t, e, p i , -q i < where 8t, e, q i , p i < are the time, energy, position, and momentum degrees of freedom. This implies that there is reciprocally conjugate relativity principle such that the rates of change of momentum must be bounded by b, where b is a universal constant. The appropriate group of dynamical symmetries that embodies this is the Canonical group CH1, 3L = UH1, 3L ≈ s HH1, 3L = SUH1, 3L ≈ s OsH1, 3L and in this theory the non-commuting space Q = CH1, 3L ê SUH1, 3L is the physical quantum space endowed with a metric that is the second Casimir invariant of the Canonical group,-2 L where 8T, E, Q i , P i , I, Y < are the generators of the algebra of OsH1, 3L = UH1L ≈ s HH1, 3L. The idea is to study the representations of the Canonical dynamical group using Mackey's theory to determine whether the representations can encompass the spectrum of particle states. The unitary irreducible representations of the Canonical group contain a direct product term that is a representation of UH1, 3L that Kalman has studied as a dynamical group for hadrons. The UH1, 3L representations contain discrete series that may be decomposed into infinite ladders where the rungs are representations of UH3L (finite dimensional) or CH2L (with degenerate UH1L ≈ SUH2L finite dimensional representations) corresponding to the rest or null frames.