Poincaré algebra and space-time critical dimensions for paraspinning strings

In this paper, we paraquantize the spinning string theory in the Neuveu-Shwarz model. Both the center of mass variables and the excitation modes of the string verify paracommutation relations. Except the $[p^μ,p^ν]$ commutator, the two other commutators of Poincaré algebra are satisfied. With the sole use of trilinear relations we find existence possibilities of spinning strings at space-time dimensions other than D=10.

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