On Simple Spinors, Null Vectors and the Orthogonal Group O(n)

TL;DR

This paper investigates the mathematical relationships between simple spinors, null vectors, and the orthogonal group O(n), providing a unified perspective on their interconnected isomorphisms.

Contribution

It offers a comprehensive analysis of the three isomorphisms linking simple spinors, null vectors, and O(n), unifying previous disparate arguments.

Findings

Clarifies the isomorphisms between simple spinors and null vectors.

Provides a unified framework for understanding the orthogonal group O(n).

Enhances mathematical understanding of spinor and vector relationships.

Abstract

We explore the three separate isomorphisms that link together simple spinors, null vectors and the orthogonal group O(n) and exploit them to look back at these arguments from a unified viewpoint.