Poincaré Algebra and Space-Time Critical Dimensions for Parabosonic Strings

We construct the parabosonic string formalism based on the paraquantization of both the center of mass variables and the excitation modes of the string. A critical study of the different commutators of the Poincaré algebra, based on the redefinition of its generators and the direct treatment using trilinear relations, is done. Space-time critical dimensions D as functions of the paraquantization order Q are obtained.