[en] A new internal position operator xi/sub μ/ = -d/sub μ/ and a new internal momentum operator π/sub μ/ are defined using an analogue of constraint Hamiltonian mechanics. The new position and momentum do not fulfill the usual relativistic Heisenberg commutation relations and both have non-commuting components, but in the non-relativistic limit they contract into the usual three-dimensional position and momentum. The new momentum π/sub μ/ is connected with an infinite dimensional generalization GAMMA/sub μ/ of the Dirac matrices, which together with the intrinsic angular momentum S/sub μ nu/ form an SO(3,2) algebra. A representation of this algebra provides the spectrum of hadron resonances, if hadrons are considered as collective vibrational and rotational excitations. A preliminary comparison between the predictions of this model and the experimental data leads to encouraging results. 22 references