Poincare algebra and space-time critical dimensions for parabosonic strings

TL;DR

This paper develops a parabosonic string formalism through paraquantization and analyzes the Poincaré algebra to determine space-time critical dimensions as functions of the paraquantization order.

Contribution

It introduces a new parabosonic string formalism and derives space-time critical dimensions based on paraquantization, expanding understanding of string theory frameworks.

Findings

Critical space-time dimensions depend on paraquantization order Q

Redefinition of Poincaré algebra generators is essential

Explicit relations between Q and space-time dimensions are established

Abstract

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 Poincar\'{e} 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.