THE OPERATOR QUANTIZATION OF THE OPEN BOSONIC STRING - FIELD ALGEBRA

Our aim in this paper is to make explicit the operator theory of the h euristic open Bosonic string and to abstract a suitable field algebra for the string. This is done on a Fock-Krein space and we examine inte grability and J-unitary implementability of all the defining transform ations of the string, i.e. time translations, gauge transformations an d Poincare transformations. The results obtained agree partially with those of Bowick and Rajeev, i.e. the gauge transformations do not leav e the Fock-Krein complex structure invariant. Once we obtained integra ted transformation groups on a suitable symplectic space for the infin itesimal transformations of the string, and proved implementability of these for the Fock-Krein representation, we are then free to define a n abstract C-algebra carrying all the algebraic information of the st ring, and to examine different representations.