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

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.