The space spinor formalism and estimates for spinor fields

TL;DR

This paper develops a method using space spinor formalism to derive estimates for spinor fields satisfying first order equations, connecting it with hyperbolicity concepts and existing strategies.

Contribution

It introduces an adaptation of the positive commutator method to first order spinor equations within the space spinor formalism.

Findings

Establishes estimates for spinor fields using the formalism.

Connects spinor hyperbolicity with existing concepts.

Provides a new perspective on first order spinor equations.

Abstract

We show how the space spinor formalism for 2-component spinors can be used to construct estimates for spinor fields satisfying first order equations. We discuss the connection of the approach presented in this article with other strategies for the construction of estimates. In addition, we recast several concepts related to the notion of hyperbolicity in the context of spinor equations. The approach described in this article can be regarded as an adaptation to first order equations of the method of positive commutators for second order hyperbolic equations.