About the Poisson Structure for D4 Spinning String

TL;DR

This paper investigates the Poisson structure of a D4 open string model with spinning variables, revealing non-uniqueness in reduction and implications for quantization, while generalizing the Regge spectrum.

Contribution

It introduces the concept of the adjunct phase space and analyzes the non-unique reduction of the Poisson structure in the D4 spinning string model.

Findings

Reduction of Poisson brackets is non-unique.

Degenerated Poisson brackets arise after reduction.

Dependence of spin on mass squared generalizes the Regge spectrum.

Abstract

The model of D4 open string with non-Grassmann spinning variables is considered. The non-linear gauge, which is invariant both Poincar\'e and scale transformations of the space-time, is used for subsequent studies. It is shown that the reduction of the canonical Poisson structure from the original phase space to the surface of constraints and gauge conditions gives the degenerated Poisson brackets. Moreover it is shown that such reduction is non-unique. The conseption of the adjunct phase space is introduced. The consequences for subsequent quantization are discussed. Deduced dependence of spin $J$ from the square of mass $\mu^2$ of the string generalizes the ''Regge spectrum`` for conventional theory.