Spins and charges in Grassmann space and Kahler spinors in space of differential forms

TL;DR

This paper explores a unified Grassmann space framework to derive spins and charges of various fields, extending the Dirac-Kahler approach to include vectors and tensors, revealing how spinors can be represented in multiple formalisms.

Contribution

It generalizes the Dirac-Kahler method to incorporate vector internal degrees of freedom and charges, providing a unified approach to spins and charges in antisymmetric tensor fields.

Findings

Unified Grassmann formulation for spins and charges.

Extended Dirac-Kahler approach to vectors and tensors.

Demonstrated how spinors appear in different formalisms.

Abstract

One of us got spins and charges of not only scalars and vectors but also of spinors out of fields, which are antisymmetric tensor fields. Kahler got spins of spinors out of differential forms, which again are antisymmetric tensor fields. Using our simple Grassmann formulation of spins and charges of either spinors or vectors and comparing it to the Dirac-Kahler formulation of spinors, we generalize the Dirac-Kahler approach to vector internal degrees of freedom and to charges of either spinors or vectors and tenzors and point out how at all spinors can appear in both approaches.