Massless Representations in Conformal Space and Their de Sitter Restrictions

TL;DR

This monograph provides a detailed, mathematically rigorous analysis of massless conformal group representations and their de Sitter restrictions, introducing a novel Clifford-split-octonion framework for spinors.

Contribution

It introduces a canonical Clifford-split-octonion framework for massless representations, unifying algebraic, spinorial, and geometric structures in conformal and de Sitter spaces.

Findings

Explicit constructions of invariant bilinear forms and Casimir operators.

Development of vertex operators and two-point functions for low-helicity fields.

Introduction of a Clifford-split-octonion framework for Majorana spinors.

Abstract

The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with fully explicit constructions. It systematically develops these representations, including the derivation of invariant bilinear forms and Casimir operators, and constructs vertex operators and two-point functions for low-helicity fields. A central and distinctive contribution is the introduction of a canonical Clifford-split-octonion framework, in which 8-component Majorana spinors are realized within an alternative composition algebra, providing a unified and intrinsically defined setting for the algebraic, spinorial, and geometric structures underlying the theory. By bridging abstract symmetry principles with concrete computational methods and physically motivated applications in quantum field theory and cosmology, the monograph advances both conceptual clarity and technical control. While primarily addressed to researchers in mathematical physics and related fields, the exposition is carefully structured to guide advanced graduate students through subtle constructions, maintaining accessibility without compromising mathematical precision.