Chiral fermions in noncommutative electrodynamics: renormalizability and dispersion

TL;DR

This paper investigates the quantization of noncommutative chiral electrodynamics, demonstrating that divergences can be renormalized through Seiberg-Witten redefinitions, and explores how noncommutativity influences chiral fermion propagation.

Contribution

It shows how to achieve renormalizability in noncommutative chiral electrodynamics via field redefinitions and analyzes the impact on fermion dispersion.

Findings

Divergences are removable by Seiberg-Witten redefinitions.

Noncommutativity induces mass and birefringence in chiral fermions.

The renormalized theory remains consistent after redefinitions.

Abstract

We analyze quantization of noncommutative chiral electrodynamics in the enveloping algebra formalism in linear order in noncommutativity parameter $\theta$. Calculations show that divergences exist and cannot be removed by ordinary renormalization, however they can be removed by the Seiberg-Witten redefinition of fields. Performing the redefinitions explicitly, we obtain renormalizable lagrangian and discuss the influence of noncommutativity on field propagation. Noncommutativity affects the propagation of chiral fermions only: half of the fermionic modes become massive and birefringent.