New spinor classes on the Graf-Clifford algebra

TL;DR

This paper introduces new classes of spinor fields on the exterior bundle with the Graf product, utilizing geometric Fierz identities to derive and analyze these classes for specific signatures and their applications.

Contribution

It develops a novel framework for constructing and studying spinor classes on the Graf-Clifford algebra, expanding the understanding of spinor fields in this geometric setting.

Findings

New spinor classes are constructed for specific signatures.

Geometric Fierz identities are used to derive properties of these classes.

Applications of the new spinor classes are discussed.

Abstract

Pinor and spinor fields are sections of the subbundles whose fibers are the representation spaces of the Clifford algebra of the forms, equipped with the Graf product. In this context, pinors and spinors are here considered and the geometric generalized Fierz identities provide the necessary framework to derive and construct new spinor classes on the space of smooth sections of the exterior bundle, endowed with the Graf product, for prominent specific signatures, whose applications are discussed.