Non-Linear Affine Embedding of the Dirac Field from the Multiplicity-Free SL(4,R) Unirreps

TL;DR

This paper explores the relationship between specific mathematical representations of SL(4,R) and non-linear affine group realizations, clarifying how spinor fields can be incorporated into a non-linear affine gauge theory of gravity.

Contribution

It establishes a connection between multiplicity-free unirreps of SL(4,R) and non-linear affine realizations, advancing the understanding of spinor fields in affine gauge theories.

Findings

Clarified the inclusion of spinorial fields in non-linear affine gauge theories

Linked SL(4,R) unirreps to non-linear realizations of the affine group

Provided mathematical framework for spinor fields in gravity models

Abstract

The correspondence between the linear multiplicity-free unirreps of SL(4, R) studied by Ne'eman and {\~{S}}ija{\~{c}}ki and the non-linear realizations of the affine group is worked out. The results obtained clarify the inclusion of spinorial fields in a non-linear affine gauge theory of gravitation.