A Covariant Framework for Generalized Spinor Dual Structures

TL;DR

This paper introduces a covariant framework for spinor duals using Clifford algebra basis elements, allowing for flexible parameterization and classification, and opening avenues for new theories in physics.

Contribution

It presents a novel, covariant formalism for spinor dual structures that generalizes previous approaches and facilitates explicit classification of spinor types.

Findings

Enables explicit construction of spinor representatives.

Recovers known spinor dual results.

Provides a flexible, parameterized formalism for spinor classification.

Abstract

In this work, we propose a novel framework for defining the dual structure of a spinor. This construction relies on the basis elements of the Clifford algebra, leading to a covariant structure that embeds the dual. The formulation includes free parameters that may be adjusted to meet specific requirements. Remarkably, it enables the explicit construction of representatives for each class within a recently proposed general classification of spinors. In addition to recovering known results, the formalism paves the way for the development of potential new theories in a manifestly covariant setting.