On complex representations of Clifford algebra

TL;DR

This paper demonstrates that complex Clifford algebra representations can be reduced to real or quaternionic forms based on space signature, influencing the nature of spinors in physics.

Contribution

It establishes a universal reduction of complex Clifford algebra representations to real or quaternionic forms depending on space signature, clarifying the nature of spinors.

Findings

Complex Clifford algebra representations reduce to real or quaternionic forms.

Supports (1,3) Minkowski space signature for physical theories.

Clarifies the nature of complex spinors in different signatures.

Abstract

We show that complex representations of Clifford algebra can always be reduced either to a real or to a quaternionic algebra depending on signature of complex space thus showing that complex spinors are unavoidably either real Majorana spinors or quaternionic spinors. We use this result to support (1,3) signature for Minkowski space.