Grassmann algebraic approach to the Neveu-Schwarz model and representation of super-Möbius algebra. (Q2752767)

On the basis of new integral representation proposed by Fairlie and Martin, we develop a mainfestly super-gauge invariant formulation of the Neveu-Schwarz model. We show that the Fairlie-Martin representation is invariant under wider transformations (super-Möbius transformations) than the usual Möbius transformations. The corresponding algebra (super-Möbius algebra) is a closed subalgebra of the super-gauge algebra. The operator formalism is reconstructed as a representation of the super-Möbius 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 conformal transformations. Finally we discuss briefly the general representation theory of the super-Möbius 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.