Spinorial discrete symmetries and adjoint structures

TL;DR

This paper explores how discrete symmetry operators can be used to construct spinorial duals, analyzing algebraic and physical constraints to identify well-defined dual structures and connecting them with spinor classifications.

Contribution

It introduces a systematic analysis of duals built from discrete symmetries and relates various spinor classifications to physical and mathematical constraints.

Findings

Certain combinations of discrete symmetries yield well-posed spinorial duals.

Connections established between Lounesto classification and other spinor classes.

Multiple possibilities for dual structures are identified and analyzed.

Abstract

Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify which combination of discrete symmetries may compose a physical and mathematical well-posed spinorial dual. In this scenario, we relate the Lounesto classification with several other spinor classification possibilities, attempting to connect classes and physical constraints. Several possibilities are investigated.