Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field

TL;DR

This paper extends gauge-covariant field decomposition to the exceptional group G(2), deriving a new non-Abelian Stokes theorem form and defining gauge-invariant magnetic monopoles with quantized magnetic charge.

Contribution

It introduces a novel gauge-covariant decomposition for G(2) Yang-Mills fields, generalizing previous methods for SU(N), and applies it to define monopoles and derive a new Wilson loop expression.

Findings

Derived a new gauge-invariant magnetic monopole definition for G(2)

Established a quantization condition for magnetic charge

Presented a generalized method applicable to semi-simple Lie groups

Abstract

We give a gauge-covariant decomposition of the Yang-Mills field with an exceptional gauge group $G(2)$, which extends the field decomposition invented by Cho, Duan-Ge, and Faddeev-Niemi for the $SU(N)$ Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of $G(2)$. The resulting new form is used to define gauge-invariant magnetic monopoles in the $G(2)$ Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semi-simple Lie group other than $SU(N)$ and $G(2)$.