N=1 de Sitter Supersymmetry Algebra

TL;DR

This paper develops a new de Sitter supersymmetry algebra using spinor fields and charge conjugation in ambient space notation, providing a novel algebraic structure relevant for theoretical physics.

Contribution

It introduces a new de Sitter superalgebra constructed via spinor fields and charge conjugation in ambient space notation, expanding the mathematical framework of supersymmetry.

Findings

Established the transformation properties of de Sitter spinor fields.

Discussed charge conjugation symmetry in de Sitter space.

Constructed a novel de Sitter superalgebra using these tools.

Abstract

Recalling the universal covering group of de Sitter, the transformation properties of the spinor fields $\psi(x)$ and ${\bar\psi}(x)$, in the ambient space notation, are presented in this paper. The charge conjugation symmetry of the de Sitter spinor field is then discussed in the above notation. Using this spinor field and charge conjugation, de Sitter supersymmetry algebra in the ambient space notation has been established. It is shown that a novel dS-superalgebra can be attained by the use of spinor field and charge conjugation in the ambient space notation.