About electrodynamics, standard model and the quantization of the electrical charge

TL;DR

This paper proposes a quantum consistency condition within electrodynamics and the standard model that naturally leads to the quantization of electric charge and hypercharge, aligning with experimental observations without external assumptions.

Contribution

It introduces a new theoretical criterion based on Ward identities and renormalization conditions that explains charge quantization in the standard model.

Findings

Derives charge quantization from internal consistency conditions.

Reproduces correct hypercharge assignments for standard model fermions.

Provides a theoretical basis for charge quantization aligned with experiments.

Abstract

The quantization of the electrical charge in the electrodynamics and of the hypercharge in the standard model are imposed in the theory based not on theoretical arguments but on the experimental observations. In this paper we propose a quantum consistency condition in a theory where Ward identities are respected that requires the quantization of the charge within the framework of the theory without external impositions. This refers to the renormalization conditions in the background gauge field method such that to ensure a correct mathematical correspondence between the bare partition function and the renormalized one. Applied to the standard model of elementary particles our criterion together with the anomaly cancellation condition leads to the correct hypercharge assignment of all standard model fermions.