Poincar\'e algebra and space-time critical dimensions for paraspinning strings

TL;DR

This paper explores the paraquantization of spinning string theory, revealing potential space-time dimensions other than the traditional D=10 by analyzing Poincaré algebra relations.

Contribution

It introduces a paraquantization approach to spinning strings and investigates their algebraic structure, suggesting alternative critical dimensions.

Findings

Poincaré algebra is satisfied except for the momentum commutator.

Existence of spinning strings in dimensions other than D=10.

Uses trilinear relations to explore critical dimensions.

Abstract

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 $[p^{\mu},p^{\nu}]$ commutator, the two other commutators of Poincar\'e 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.