Real-time correlation functions in the O(N) model from the functional renormalization group

In this paper, ‘massless’ spin- $frac{3}{2}$ fields in the de Sitter space are considered. This work is a 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 an 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 a 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.