Renormalization of the QED of self-interacting second order spin 1/2 fermions

TL;DR

This paper investigates the one-loop renormalization of a second-order spin 1/2 fermion electrodynamics model, demonstrating its renormalizability for arbitrary gyromagnetic factors and connecting it to known models like QED and Nambu-Jona-Lasinio.

Contribution

It extends the renormalization analysis of second-order fermion electrodynamics to arbitrary gyromagnetic factors and includes fermion self-interactions, generalizing previous results.

Findings

Model is renormalizable for any gyromagnetic factor g within perturbative limits.

Recovers pure QED of second order fermions at g=±2.

Reduces to a Nambu-Jona-Lasinio-like model without electromagnetic interaction.

Abstract

We study the one-loop level renormalization of the electrodynamics of spin 1/2 fermions in the Poincar\'e projector formalism, in arbitrary covariant gauge and including fermion self-interactions, which are dimension four operators in this framework. We show that the model is renormalizable for arbitrary values of the tree level gyromagnetic factor g within the validity region of the perturbative expansion, \alpha g^2 << 1. In the absence of tree level fermion self-interactions, we recover the pure QED of second order fermions, which is renormalizable only for |g|=2. Turning off the electromagnetic interaction we obtain a renormalizable Nambu-Jona-Lasinio-like model with second order fermions in four space-time dimensions.