On Spinors of Zero Nullity

TL;DR

This paper establishes a precise condition for spinors to have zero nullity, exploring their relationship with conjugate spinors and null vectors, advancing the understanding of spinor nullity in mathematical physics.

Contribution

It provides a necessary and sufficient criterion for spinors to have nullity zero, deepening the theoretical understanding of spinor properties and their conjugates.

Findings

Derived a condition for zero nullity spinors

Analyzed relations between spinors and their conjugates

Enhanced understanding of spinor-null vector interactions

Abstract

We present a necessary and sufficient condition for a spinor $\omega$ to be of nullity zero, i.e. such that for any null vector $v$, $v \omega \ne 0$. This dives deeply in the subtle relations between a spinor $\omega$ and $\omega_c$, the (complex) conjugate of $\omega$ belonging to the same spinor space.