Grassmann Algebraic Approach to the Neveu-Schwarz Model and Representation of Super-Mobius Algebra

On the basis of new integral representation proposed by Fairlie and Martin, we develop a manifestly super-gauge invariant formulation of the Neveu-Schwarz model. We show that the Fairlie-Martin representation is invariant under wider trafisformations (super-Mobius transformations) than the usual Mobius transformations. The corresponding algebra (super Mobius algebra) is a closed subalgebra of the super-gauge algebra. The operator formalism is reconstructed as a representation of the super-Mobius algebra. As a generalization of our formulation, we introduce closed-string emission vertices for the Neveu-Schwarz open-string which are manifestly covariant under the super-gauge transformations as well as the confotmal transformations. Finally we discuss briefly the general representation theory of .the s~per Mobius algebra. Unfortunately, the representation appeared in the Neveu-Schwarz model is essentially unique as the representation of the full super-gauge algebra. However, two types of_ the mass spectrum are possible.