Operator Methods in the Superstring Theory.

Two aspects of the superstring theory are studied in the operator language. The interaction between the open string and the closed string is discussed in the Neveu -Schwarz-Ramond formalism. Transition amplitudes are given by the overlap vertex of the string wave functions. To ensure the BRST invariance, a supercurrent-like operator insertion is required. By shifting the picture of the open string vacuum, this insertion is identified as the picture changing operator. Its role is to keep both the open string vacuum and the closed string vacuum in the same picture. This is a consequence of the nonzero superghost background charge in the RNS formalism. Also, a canonical quantization of the Green-Schwarz superstring is pursued here. A new method of operator quantization developed by Batalin and Fradkin is applied to the heterotic string in a semi-light cone gauge. Using a normal ordering regularization, it is shown that quantum anomalies cancel at the critical dimension, D = 10.