A Discussion on Dirac Field Theory, No-Go Theorems and Renormalizability

TL;DR

This paper examines Dirac field equations coupled with electrodynamics, exploring how torsion affects spinorial solutions and discussing implications for the renormalizability of point-like particles.

Contribution

It provides a detailed analysis of the incompatibility between certain spinorial solutions and torsion, and discusses their impact on the renormalizability problem.

Findings

Spinorial solutions are incompatible with torsion.

Implications for the renormalizability of point particles.

Framework for future studies on Dirac fields with torsion.

Abstract

We study Dirac field equations coupled to electrodynamics with metric and torsion fields: we discuss how special spinorial solutions are incompatible with torsion; eventually these results will be used to sketch a discussion on the problem of renormalizability of point-like particles.