Reformulation of the Georgi-Glashow model and some constraints on its classical fields

TL;DR

This paper reformulates the SU(2) Georgi-Glashow model using a new field decomposition approach, extending Cho's method, to better understand the model's classical fields and constraints.

Contribution

It introduces a novel decomposition of the Georgi-Glashow model's fields, generalizes Cho's extended decomposition, and explores constraints like the condensate phase.

Findings

Derived a new Lagrangian based on the decomposition

Interpreted the field $ extbf{n} $ as the scalar field's color direction

Connected the decomposition to Faddeev and Niemi's proposal

Abstract

We study the SU(2) Georgi-Glashow model and suggest a decomposition for its fields and obtain a Lagrangian based on new variables. We use Cho's restricted decomposition as a result of a vacuum condition of the Georgi-Glashow model. This model with no external sources leads us to the Cho extended decomposition. We interpret the puzzling field, $ \textbf{n} $, in Cho's decomposition as the color direction of the scalar field in the Georgi-Glashow model. We also study another constraint, condensate phase, and generalize Cho's extended decomposition. Finally, we argue about a decomposition form that Faddeev and Niemi proposed in this constrained Georgi-Glashow model.