A quasi-Lie bialgebra formulation of the Pohlmeyer-Rehren Poisson algebra

TL;DR

This paper reformulates the Pohlmeyer-Rehren Poisson algebra within a quasi-Lie bialgebra framework, providing solutions for specific bivector ranks, advancing the algebraic understanding of string theory invariants.

Contribution

It introduces a quasi-Lie bialgebra formulation for the Pohlmeyer-Rehren algebra and solves the quantization problem for bivectors of rank 1 and 2.

Findings

Successfully formulated the QLBA structure based on a symmetric bivector.

Provided explicit solutions for the quantization problem when bivector rank is 1 or 2.

Enhances algebraic methods in string theory invariant analysis.

Abstract

We present a quasi-Lie bialgebra (QLBA) quantization problem which comes from an algebraic reformulation of the Nambu-Goto string theory and invariant charges by Pohlmeyer and Rehren. This QLBA structure depends on a symmetric bivector (coming from a Minkowski metric) and is built on the free Lie algebra on a finite dimensional vector space. We solve this problem when the bivector has rank 1 or 2.