On an Alternative Approach to the Relation between Bosons and Fermions: Employing Clifford Space

TL;DR

This paper investigates a novel framework where physics occurs in Clifford space, allowing transformations that mix bosons and fermions through operators acting on Clifford algebra-valued fields, offering a new perspective on their relation.

Contribution

It introduces a Clifford space-based approach where bosonic and fermionic fields are unified via polyvector fields, enabling transformations between them.

Findings

Polyvector fields can be expanded into bosonic or fermionic components.

Transformations in Clifford space can mix bosons and fermions.

Scalar fields can transform into mixtures of bosonic and fermionic fields.

Abstract

We further explore the idea that physics takes place in Clifford space which should be considered as a generalization of spacetime. Following the old observation that spinors can be represented as members of left ideals of Clifford algebra, we point out that the transformations which mix bosons and fermions could be represented by means of operators acting on Clifford algebra-valued (polyvector) fields. A generic polyvector field can be expanded either in terms of bosonic, or in terms of fermionic fields. In particular, a scalar field can transform into a mixture of bosonic and/or fermionic fields.