A Tomonaga-Schwinger-Dirac formulation for string theories

A Tomonaga-Schwinger-Dirac formulation of the first quantized free bosonic string theory is presented in which all the Virasoro operators have simple geometric meanings. In a corresponding second quantized version, the "chordal" gauge transformations on the free string field, which generate linearized gauge transformations of spacetime fields, become natural transformations in an extended loop space. The geometrical nature of these transformations may allow them to be more easily generalized to the nonlinear transformations of the interacting string field theory.