The Presentation of the Algebra of Observables of the Closed Bosonic String in 1+3 Dimensions: Calculation up to Order \hbar^7

TL;DR

This paper develops a quantization method for the observable algebra of closed bosonic strings in 1+3 dimensions, computing quantum corrections up to order  and analyzing the algebraic structure and relations.

Contribution

It introduces a detailed calculation of quantum corrections to the algebra of observables up to order , revealing structural changes and the absence of higher-order relations.

Findings

Quantum corrections break the classical algebra's semidirect splitting.

No independent relations of order  are found.

The algebra's structure is significantly altered at quantum level.

Abstract

We proceed with the investigation of a method of quantization of the observable sector of closed bosonic strings. For the presentation of the quantum algebra of observables the construction cycle concerning elements of order \hbar^6 has been carried out. We have computed the quantum corrections to the only generating relation of order \hbar^6. This relation is of spin-parity J^P=0^+. We found that the quantum corrections to this relation break the semidirect splitting of the classical algebra into an abelian, infinitely generated subalgebra a and a non-abelian, finitely generated subalgebra U. We have established that there are no ("truly independent") generating relations of order \hbar^7.