Reparametrization Invariant Operators in String Field Theory.

In this study, the role of the reparametrization group in the field theory of strings is examined. Representations and direct product rules are constructed for both the bosonic and supersymmetric reparametrization algebras. This group theory is applied to free open bosonic string field theory. A catalog is made of the various invariant operators which may be formed. These are found to include a previously unknown symmetric tensor whose trace is the BRST charge. It is found that only certain subsets of the projections of this tensor are closed algebraically. The possible subgroups of the Lorentz group which may be left unbroken by the choice of these subsets are classified. Finally, reparametrization invariance is discussed in the context of the interacting open string theory of Witten. It is argued that in this theory, reparametrization invariance is hidden by a parametrization dependent choice of phases in a set of basis wave functionals. An alternative, completely equivalent, version of this theory is constructed, which does possess manifest reparametrization invariance; however, the interaction in the new formulation has an apparently nonlocal form.