"Massless'' Spin-$\frac{3}{2}$ Fields in the de Sitter Space

Abstract

In this paper, the ``massless" spin-$\frac{3}{2}$ fields in the de Sitter space are considered. This work is in the continuation of a previous paper devoted to the quantization of the de Sitter ``massive" spin-$\frac{3}{2}$ fields. Due to the appearance of gauge invariance and indefinite metric, the covariant quantization of the ``massless" spin-$\frac{3}{2}$ fields requires an indecomposable representation of the de Sitter group. The gauge fixing corresponding to the simplest Gupta-Bleuler structure is used, and gauge invariant field is discussed. The field equation is obtained by using the Casimir operator of the de Sitter group. The solutions are written in terms of the coordinate-independent de Sitter plane waves. Finally, the generalized two-point function is calculated.