THE PRESENTATION OF THE QUANTUM ALGEBRA OF OBSERVABLES OF THE CLOSED BOSONIC STRING IN 1+3 DIMENSIONS: THE EXACT QUANTIZED GENERATING RELATIONS OF ORDERS ℏ6 AND ℏ7

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 ℏ6 has been carried out. We have computed the quantum corrections to the only generating relation of order ℏ6. This relation is of spin-parity JP = 0+. We found that the quantum corrections to this relation break the semidirect splitting of the classical algebra into an Abelian, infinitely generated subalgebra [Formula: see text] and a non-Abelian, finitely generated subalgebra [Formula: see text]. We have established that there are no ("truly independent") generating relations of order ℏ7.